[3, 2, 4, 1, 1, 5, 1, 2]
 ^

[3, 2, 4]

3 -> [3, 2, 4]
2 -> [2, 4]
4 -> [4, 1, 1, 5]
1 -> [1]
1 -> [1]
5 -> [5, 1, 2]
1 -> [1]
2 -> [2]

[3, 2, 4, 1, 1, 5, 1, 2]
                ^  ^  ^  ^  ^

[3, 2, 4]     -> 9
[2, 4]        -> 6
[4, 1, 1, 5]  -> 11
[1]           -> 1
[1]           -> 1
[5, 1, 2]     -> 8
[1]           -> 1
[2]           -> 2

[9, 6, 11, 1, 1, 8, 1, 2]

[1, 2, 3, 4, 5] -> [1, 5, 12, 9, 5]
[3, 3, 3, 3, 3, 3, 3, 3] -> [9, 9, 9, 9, 9, 9, 6, 3]
[5, 1, 2, 4, 1] -> [13, 1, 6, 5, 1]
[1] -> [1]

ṫJḣ"ḅ1

ṫJḣ"ḅ1  Main link. Argument: A (array)

 J      Index; yield the 1-based indices of A.
ṫ       Tail; map k to the postfix of A that begins with the k-th element.
  ḣ"    Vectorized head; for each k in A, truncate the corr. postfix to length k.
    ḅ1  Convert the resulting slices from base 1 to integer.

lambda X:[sum(X[i:i+k])for i,k in enumerate(X)]

f l@(x:y)=sum(take x l):f y
f x=x

+/@{."_1].

f =: +/@{."_1].
   f 3 2 4 1 1 5 1 2
9 6 11 1 1 8 1 2
   f 1 2 3 4 5
1 5 12 9 5

+/@{."_1].  Input: A
        ].  Get each suffix of A from longest to shortest
   {."_1     For each value in A, take that many values from its corresponding suffix
+/@          Sum that group of values taken from that suffix
             Return the sums

d+
$*
M!&`b1(1)*(?<-1>,1+)*
M%`1
¶
,

Tr@Take[#,UpTo@#&@@#]&/@Drop[#,t-1]~Table~{t,Length@#}&

f = %; f /@ {{1, 2, 3, 4, 5}, {3, 3, 3, 3, 3, 3, 3, 3}, {5, 1, 2, 4, 1}, {1}}

(*    {{1, 5, 12, 9, 5}, {9, 9, 9, 9, 9, 9, 6, 3}, {13, 1, 6, 5, 1}, {1}}    *)

[D¬£Oˆ¦Ž

[         # infinite loop
 D        # duplicate current list
  ¬       # get head of list
   £      # get that many elements from list
    O     # sum
     ˆ    # add to global array
      ¦   # remove first element of list
       Ž  # break if stack is empty
          # implicitly push and print global array

.es:Qk+b

f(A)->put(1,1),L=lists,[L:sum(L:sublist(A,put(1,get(1)+1),X))||X<-A].

FKo>i<s

- o = 0
F       - for i in input:
  o     -    o+=1
   >    -    input[o:]
    i<  -   ^[:i]
      s -  sum(^)

Function e(g())
Dim h()
k=LBound(g)
l=UBound(g)
ReDim h(k To l)
On Error Resume Next
For i=k To l
For j=i To i+g(i)-1
h(i)=h(i)+g(j)
Next
Next
e=h
End Function

ms<~tQ

ms<~tQ
ms<~tQdQ    Implicit variable introduction
            Implicit: Q = eval(input())
m      Q    Map d over the input, Q
  <  Qd     Take the first d elements of Q
 s          Sum them
   ~tQ      Afterwards, set Q to the tail of Q, removing the first element.

let f(A:int[])=[for i in 0..A.Length-1->Seq.skip i A|>Seq.truncate A.[i]|>Seq.sum]

f=([a,...t],n)=>a&&n?a+f(t,n-1):0;g=([a,...t],r=[])=>a?g(t,[...r,a+f(t,a-1)]):r

int[]s(List<int>a)=>a.Select((n,i)=>a.GetRange(i,Math.Min(n,a.Count-i)).Sum()).ToArray();

.v|h~l(A:Tc?;A?)b:0&~b.h~+A

.v           Input = Output = []
|            Or
  h~l          A is a list, its length is the value of the first element of the Input
  (
    A:Tc?        The concatenation of A with another list T results in the Input
  ;            Or
    A?           A = Input
  )
  b:0&         Call recursively on Input minus the first element
  ~b.          Output is the output of that call with an extra element at the beginning
  h~+A         That extra element is the sum of the elements of A

{+/¨⍵↑∘⌽¨⌽,⌽⍵}

{⌽+/¨(-↑¨,)⌽⍵}

<?foreach($a=$_GET[a]as$i=>$v)echo array_sum(array_slice($a,$i,$v)),"
";

function f($a){foreach($a as$i=>$v)$r[]=array_sum(array_slice($a,$i,$v));return$r;}

function p($a){foreach($c=$r=$a as$i=>$v)for($k=$i;$k--;)if(--$a[$k]>0)$r[$k]+=$v;return$r;}

<?foreach($a=$r=$c=$_GET[a]as$i=>$v)for($k=$i;$k--;)if(--$c[$k]>0)$r[$k]+=$v;print_r($r);

{sum each(til[count x],'x)sublist:x}

q){sum each(til[count x],'x)sublist:x}3 2 4 1 1 5 1 2
9 6 11 1 1 8 1 2

md{z:l-g:c;+c;q:c;};:1:l;

m                  :1:l;   #loop over entire input
                           #set each value to...
 d{               }        #the sum of...
   z:l-g:c:+c;q:c;         #the input cropped to
                           #the length of the value in the cell

n=>_.From(n).Select((v,i)=>_.From(n).Slice(i,i+v).Sum()).ToArray()

(defn f[[b & r]](concat[(apply + b(take(dec b)r))](if r(f r))))

fGy+!-R0<G*!s

f     % Take input implicitly. Indices of nonzero elements: this gives [1 2 ... n]
      % where n is input size
G     % Push input again
y     % Push a copy of [1 2 ... n]
+     % Add. Gives [a+1 b+2...] where [a b...] is the input
!     % Transpose into a column vector
-     % Subtraction with broadcast. Gives 2D array
R     % Keep upper triangular part, making the rest of entries 0
0<    % True for negative entries. Each row corresponds to a substring sum.
      % For each row, this gives true for the entries of the input that make up
      % that substring sum. Each row is thus a mask to select entries of the input
G     % Push input again
*     % Multiply with broadcast. This multiplies the input times each row
!s    % Sum of each row. Implicitly display

Console.Write(String.Join(",",a.Select((v,i)=>a.Skip(i).Take(v).Sum().ToString()).ToArray()));