nd[y_, a_, b_, n_] := (Binomial[b - a + 1, y]*Sum[((-1)^i)*Binomial[y, i]*((y - i)/(b - a + 1))^n, {i, 0, y}]);
Blend[{Black, Purple, Blue, Green, Yellow, Orange, Red, White}, ColorScaling -> False]
Manipulate[
 ArrayPlot[Table[nd[y, 1, K, N], {K, 1, 25}, {N, 1, 25}],
  ColorFunction -> mycolorfun, DataReversed -> True, Frame -> True,
  FrameTicks -> Automatic,
  FrameLabel -> {Rotate["K", -90 Degree], "N"}], {y, 1, 15, 1}]

nd[15, 1, 21, 25.0]
(out) 0.268495