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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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