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A292164 Expansion of Product_{k>=1} (1 - k^2*x^k). 4
1, -1, -4, -5, -7, 27, 17, 167, 110, -42, 10, -706, -4001, -3915, 3079, -18640, 9869, 21403, 130565, 107250, -15661, 420664, 599540, -161785, -1232833, -5836888, -5129796, 6516714, -29068180, -14953045, -41490510, 20261320, 30395771, 441235155, 205289550 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

FORMULA

Convolution inverse of A077335.

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

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

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

    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(prod(n=1, N, 1-n^2*x^n))

CROSSREFS

Column k=2 of A292166.

Cf. A022629, A022661, A077335, A092484.

Sequence in context: A049896 A029520 A123368 * A178439 A214584 A198131

Adjacent sequences:  A292161 A292162 A292163 * A292165 A292166 A292167

KEYWORD

sign

AUTHOR

Seiichi Manyama, Sep 10 2017

STATUS

approved

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Last modified January 23 04:16 EST 2020. Contains 331168 sequences. (Running on oeis4.)