%I #13 Nov 16 2022 04:58:32

%S 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,

%T 4743,1956,1,1,49,671,5629,27313,52525,13699,1,1,64,1105,12736,100045,

%U 440896,683657,109600,1,1,81,1695,25099,280581,2122449,8390875,10256775

%N Array read by antidiagonals: see A128195 for details.

%H P. Luschny, <a href="http://www.luschny.de/math/seq/variations.html">Variants of Variations</a>.

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

%e Array begins:

%e [0] 1, 1, 1, 1, 1, 1, 1, 1, 1

%e [1] 1, 4, 15, 64, 325, 1956, 13699, 109600, 986409

%e [2] 1, 9, 65, 511, 4743, 52525, 683657, 10256775, 174369527

%e [3] 1, 16, 175, 2020, 27313, 440896, 8390875, 184647364, 4616348125

%e [4] 1, 25, 369, 5629, 100045, 2122449, 53163625, 1542220261, 50895431301

%e [5] 1, 36, 671, 12736, 280581, 7376356, 229151411, 8252263296, 338358810761

%p 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

%t 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 *)

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

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

%K nonn,tabl,easy

%O 0,5

%A _N. J. A. Sloane_, Feb 28 2007

%E More terms from _R. J. Mathar_, May 18 2007