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A292165 Expansion of Product_{k>=1} 1/(1 + k^2*x^k). 3
1, -1, -3, -6, 6, 5, 40, 11, 226, -516, -186, -844, 3731, -3734, 814, -33819, 85660, -46022, 210342, -411678, 593996, -2980156, 2076721, -3445584, 40785410, -37503158, 98085, -271846888, 336918770, -295108832, 2178341296, -2404059340, 6127604258 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..3145

FORMULA

Convolution inverse of A092484.

From Vaclav Kotesovec, Sep 10 2017: (Start)

a(n) ~ (-1)^n * c * 3^(2*n/3), where

c = 0.717271758899891528435966115495396784611147877234945... if mod(n,3)=0

c = 0.387695187106751505296020614217498222070185848125472... if mod(n,3)=1

c = 0.241939482775588594057384356004734639024152664456553... if mod(n,3)=2

(End)

G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^k*j^(2*k)*x^(j*k)/k). - Ilya Gutkovskiy, Jun 18 2018

MAPLE

b:= proc(n, i) option remember; (m->

      `if`(m<n, 0, `if`(n=m, i!^2, b(n, i-1)+

      `if`(i>n, 0, i^2*b(n-i, i-1)))))(i*(i+1)/2)

    end:

a:= proc(n) option remember; `if`(n=0, 1,

      -add(b(n-i$2)*a(i$2), i=0..n-1))

    end:

seq(a(n), n=0..40);  # Alois P. Heinz, Sep 10 2017

PROG

(PARI) N=66; x='x+O('x^N); Vec(1/prod(n=1, N, 1+n^2*x^n))

CROSSREFS

Cf. A077335, A092484.

Sequence in context: A179949 A187601 A113737 * A327576 A040006 A155067

Adjacent sequences:  A292162 A292163 A292164 * A292166 A292167 A292168

KEYWORD

sign

AUTHOR

Seiichi Manyama, Sep 10 2017

STATUS

approved

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Last modified November 19 18:39 EST 2019. Contains 329323 sequences. (Running on oeis4.)