A126062 Array read by antidiagonals: see A128195 for details.

1, 1, 1, 1, 4, 1, 1, 9, 15, 1, 1, 16, 65, 64, 1, 1, 25, 175, 511, 325, 1, 1, 36, 369, 2020, 4743, 1956, 1, 1, 49, 671, 5629, 27313, 52525, 13699, 1, 1, 64, 1105, 12736, 100045, 440896, 683657, 109600, 1, 1, 81, 1695, 25099, 280581, 2122449, 8390875, 10256775

Offset: 0

Author

N. J. A. Sloane, Feb 28 2007

Keywords

• nonn
• tabl
• easy

Examples

			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
		

Links

• P. Luschny, Variants of Variations.

Crossrefs

The second row counts the variations of n distinct objects A007526.

The second column is sequence A000290. The third column is sequence A005917.

Programs

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 *)

Formula

T(k, n) = (n*k+1)*(T(k, n-1) + k^n), T(k, 0) = 1. - Peter Luschny, Feb 26 2007

Extensions

More terms from R. J. Mathar, May 18 2007