A153658 Triangle read by rows: A(n,k)=A(n - 1, k - 1) + A(n - 1, k) + (n + 1)*(n + 2)*A(n - 2, k - 1).

2, 120, 120, 2, 1436, 2, 2, 5038, 5038, 2, 2, 5124, 70388, 5124, 2, 2, 5238, 357640, 357640, 5238, 2, 2, 5384, 731806, 5783216, 731806, 5384, 2, 2, 5566, 1208610, 38702622, 38702622, 1208610, 5566, 2, 2, 5788, 1806416, 120409892, 713559004

Offset

1,1

Comments

Row sums are (2*(n + 3)!) except for n=1 which is 2: {2, 240, 1440, 10080, 80640, 725760, 7257600, 79833600, 958003200, 12454041600}.

Links

Table of n, a(n) for n=1..41.

Example

{2},
{120, 120},
{2, 1436, 2},
{2, 5038, 5038, 2},
{2, 5124, 70388, 5124, 2},
{2, 5238, 357640, 357640, 5238, 2},
{2, 5384, 731806, 5783216, 731806, 5384, 2},
{2, 5566, 1208610, 38702622, 38702622, 1208610, 5566, 2},
{2, 5788, 1806416, 120409892, 713559004, 120409892, 1806416, 5788, 2},
{2, 6054, 2546916, 281752828, 5942715000, 5942715000, 281752828, 2546916, 6054, 2}

Mathematica

Clear[A]; A[2, 1] := A[2, 2] = (5)!;
A[3, 2] = 2*(6)! - 4; A[4, 2] = A[4, 3] = (7)! - 2;
A[n_, 1] := 2; A[n_, n_] := 2;
A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (n + 1)*(n + 2)*A[n - 2, k - 1];
a = Table[A[n, k], {n, 10}, {k, n}]; Flatten[a]
Table[Apply[Plus, a[[n]]], {n, 1, 10}];
Table[Apply[Plus, a[[n]]]/(2*(n + 3)!), {n, 1, 10}]

Crossrefs

Sequence in context: A221231 A243512 A165163 * A073785 A102355 A206355

Adjacent sequences: A153655 A153656 A153657 * A153659 A153660 A153661

Keyword

nonn,tabl

Author

Roger L. Bagula, Dec 30 2008

Extensions

Edited by N. J. A. Sloane, Jun 02 2009

Status

approved