A319576 a(n) = (4/15)*n*(n - 1)*(n^3 - 9*n^2 + 26*n - 9).

0, 0, 8, 24, 48, 112, 312, 840, 2016, 4320, 8424, 15224, 25872, 41808, 64792, 96936, 140736, 199104, 275400, 373464, 497648, 652848, 844536, 1078792, 1362336, 1702560, 2107560, 2586168, 3147984, 3803408, 4563672, 5440872, 6448000, 7598976, 8908680, 10392984

Offset: 0

Author

Peter Luschny, Oct 01 2018

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A000012 (m=0), A005843 (m=1), A046092 (m=2), A130809 (m=3), A319575 (m=4), this sequence (m=5), A319577 (m=6).

Column n=5 of A122141.

Cf. A319574.

Programs

Maple

a := n -> (4/15)*n*(n - 1)*(n^3 - 9*n^2 + 26*n - 9):
seq(a(n), n=0..41);

Mathematica

A319576[n_] := 4/15*n*(n-1)*(n^3-9*n^2+26*n-9); Array[A319576, 50, 0] (* or *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 0, 8, 24, 48, 112}, 50] (* Paolo Xausa, Feb 20 2024 *)

PARI

concat([0,0], Vec(8*x^2*(1 - 3*x + 3*x^2 + 3*x^3) / (1 - x)^6 + O(x^40))) \\ Colin Barker, Oct 02 2018

Formula

a(n) = [x^5] JacobiTheta3(x)^n.

a(n) = A319574(n,5).

From Colin Barker, Oct 02 2018: (Start)

G.f.: 8*x^2*(1 - 3*x + 3*x^2 + 3*x^3) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.

(End)