A245940 (2n^7 + 4n^6 - n^5 - 4n^4 - n^3) / 24.

0, 0, 17, 279, 1960, 8875, 30555, 87122, 216384, 483570, 994125, 1909985, 3469752, 6013189, 10010455, 16096500, 25111040, 38144532, 56590569, 82205115, 117173000, 164182095, 226505587, 308092774, 413668800, 548843750, 720231525, 935578917, 1203905304

Offset

0,3

Comments

For n > 0: sum of n-th row of triangle A245826.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = n^3*(2*n^3 + 2*n^2 - 3*n - 1)*(n + 1)/24 = n^3*(n - 1)*(n + 1)*(2*n^2 + 4*n + 1)/24.

G.f.: x^2*(x^4 + 55*x^3 + 204*x^2 + 143*x + 17) / (x - 1)^8. - Colin Barker, Aug 08 2014

Maple

A245940:=n->(2*n^7 + 4*n^6 - n^5 - 4*n^4 - n^3) / 24: seq(A245940(n), n=0..30); # Wesley Ivan Hurt, Aug 09 2014

Mathematica

Table[(2 n^7 + 4 n^6 - n^5 - 4 n^4 - n^3)/24, {n, 0, 30}] (* Vincenzo Librandi, Aug 09 2014 *)
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 0, 17, 279, 1960, 8875, 30555, 87122}, 30] (* Harvey P. Dale, Apr 19 2018 *)

Prog

(Haskell)
a245940 n = n^3 * (2 * n^3 + 2 * n^2 - 3 * n - 1) * (n + 1) `div` 24
(PARI)
concat([0, 0], Vec(x^2*(x^4+55*x^3+204*x^2+143*x+17)/(x-1)^8 + O(x^100))) \\ Colin Barker, Aug 08 2014
(Magma) [(2*n^7 + 4*n^6 - n^5 - 4*n^4 - n^3) / 24: n in [0..30]] // Vincenzo Librandi, Aug 09 2014

Crossrefs

Sequence in context: A029811 A113076 A159503 * A188063 A012235 A196743

Adjacent sequences: A245937 A245938 A245939 * A245941 A245942 A245943

Keyword

nonn,easy

Author

Reinhard Zumkeller, Aug 07 2014

Status

approved