A316087 Expansion of 1/(1 + Sum_{k>=1} k^2 * x^k).

1, -1, -3, -2, 7, 19, 8, -53, -119, -18, 387, 727, -112, -2745, -4315, 2238, 18991, 24715, -24296, -128461, -135023, 219502, 850635, 688239, -1806560, -5515441, -3116403, 14022398, 34994967, 10783939, -104389592, -216919973, -5497639, 752295022, 1309660627

Offset: 0

Author

Seiichi Manyama, Jun 24 2018

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..3000
• Index entries for linear recurrences with constant coefficients, signature (2, -4, 1).

Crossrefs

1/(1+ Sum_{k>=1} k^m * x^k): A163810 (m=1), this sequence (m=2), A316088 (m=3).

Cf. A253909, A316086.

Programs

PARI

N=99; x='x+O('x^N); Vec(1/(1+sum(k=1, sqrtint(N), k^2*x^k)))

Formula

Convolution inverse of A253909.

G.f.: (x-1)^3/(x^3-4*x^2+2*x-1).

a(0) = 1; a(n) = -Sum_{k=1..n} k^2 * a(n-k). - Ilya Gutkovskiy, Feb 02 2021