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

0,5

Links

Table of n, a(n) for n=0..52.

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

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

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

Sequence in context: A039756 A126065 A299427 * A243608 A219207 A157108

Adjacent sequences: A126059 A126060 A126061 * A126063 A126064 A126065

Keyword

nonn,tabl,easy

Author

N. J. A. Sloane, Feb 28 2007

Extensions

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

Status

approved