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A316087
Expansion of 1/(1 + Sum_{k>=1} k^2 * x^k).
5
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
0,3
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
PROG
(PARI) N=99; x='x+O('x^N); Vec(1/(1+sum(k=1, sqrtint(N), k^2*x^k)))
CROSSREFS
1/(1+ Sum_{k>=1} k^m * x^k): A163810 (m=1), this sequence (m=2), A316088 (m=3).
Sequence in context: A344211 A104528 A177115 * A196537 A173099 A111928
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jun 24 2018
STATUS
approved