A130857 a(n) = (n-1)*n*(n+1)*(n+2)*(2n+11)/120.

0, 3, 17, 57, 147, 322, 630, 1134, 1914, 3069, 4719, 7007, 10101, 14196, 19516, 26316, 34884, 45543, 58653, 74613, 93863, 116886, 144210, 176410, 214110, 257985, 308763, 367227, 434217, 510632, 597432, 695640, 806344, 930699, 1069929

Offset: 1

Author

Roger L. Bagula, Jul 22 2007

Keywords

• nonn

Comments

The motivation for this sequence is the triple sum Sum[Sum[Sum[k^2-1,{k,1,m}],{m,1,j}],{j,1,n}], which can be simplified into the polynomial term given as definition.

Crossrefs

Cf. A117662.

Programs

Mathematica

Table[(n - 1)*n(n + 1)*(n + 2)*(2*n + 11)/120, {n, 1, 35}]
Times@@#*(2#[[2]]+11)/120&/@Partition[Range[0,40],4,1] (* Harvey P. Dale, Oct 28 2012 *)

Formula

G.f.: -x^2*(x-3)/(-1+x)^6. - R. J. Mathar, Nov 14 2007

Extensions

Edited and extended by N. J. A. Sloane, Jul 26 2007