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# Untitled

a guest Jun 15th, 2019 59 Never
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1. f[m_, n_] := f[m, n] =
2.   If[m == 0 || n == 0, 1,
3.    If[m <= n,
4.     (m + 1)^n *
5.       InterpolatingPolynomial[
6.        Table[{k, f[m, k]/(m + 1)^k}, {k, 0, m - 1}], x] /. x -> n,
7.     (n + 1)^m*
8.       InterpolatingPolynomial[
9.        Table[{k, f[k, n]/(n + 1)^k}, {k, 0, n - 1}], x] /. x -> m]]
10.
11. 1,1,1,1,1,1,1,1,1,1,1
12. 1,2,4,8,16,32,64,128,256,512,1024
13. 1,4,15,54,189,648,2187,7290,24057,78732,255879
14. 1,8,54,328,1856,9984,51712,260096,1277952,6160384,29229056
15. 1,16,189,1856,16145,129000,968125,6925000,47690625,318500000,2073828125
16. 1,32,648,9984,129000,1475856,15450912,151201728,1403288064,12479546880,107152782336
17. 1,64,2187,51712,968125,15450912,219682183,2862173104,34828543449,401200569280,4418300077219
18. 1,128,7290,260096,6925000,151201728,2862173104,48658878080,760774053888,11122973573120,153936323805184
19. 1,256,24057,1277952,47690625,1403288064,34828543449,760774053888,15047189968833,274908280855680,4707029151392121
20. 1,512,78732,6160384,318500000,12479546880,401200569280,11122973573120,274908280855680,6199170628499200,129708290461760000
21. 1,1024,255879,29229056,2073828125,107152782336,4418300077219,153936323805184,4707029151392121,129708290461760000,3283463201858585471
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