OFFSET
0,5
LINKS
P. Luschny, Variants of Variations.
FORMULA
T(k, n) = (n*k+1)*(T(k, n-1) + k^n), T(k, 0) = 1. - Peter Luschny, Feb 26 2007
EXAMPLE
Array begins:
[0] 1, 1, 1, 1, 1, 1, 1, 1, 1
[1] 1, 4, 15, 64, 325, 1956, 13699, 109600, 986409
[2] 1, 9, 65, 511, 4743, 52525, 683657, 10256775, 174369527
[3] 1, 16, 175, 2020, 27313, 440896, 8390875, 184647364, 4616348125
[4] 1, 25, 369, 5629, 100045, 2122449, 53163625, 1542220261, 50895431301
[5] 1, 36, 671, 12736, 280581, 7376356, 229151411, 8252263296, 338358810761
MAPLE
A126062 := proc(k, n) if n = 0 then 1 ; else (n*k+1)*(A126062(k, n-1)+k^n) ; fi ; end: for diag from 0 to 10 do for k from diag to 0 by -1 do n := diag-k ; printf("%d, ", A126062(k, n)) ; od ; od ; # R. J. Mathar, May 18 2007
MATHEMATICA
a[_, 0] = 1; a[k_, n_] := a[k, n] = (n*k+1)*(a[k, n-1]+k^n); Table[a[k-n, n], {k, 0, 10}, {n, 0, k}] // Flatten (* Jean-François Alcover, Jan 08 2014 *)
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, Feb 28 2007
EXTENSIONS
More terms from R. J. Mathar, May 18 2007
STATUS
approved