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A307484 Expansion of Product_{k>=1} 1/(1+x^k)^((-1)^k*k^2). 1
1, 1, -4, 5, 3, -17, 33, -61, 67, 63, -392, 803, -1070, 898, 482, -4449, 11362, -18630, 21105, -11067, -24871, 103562, -227004, 359040, -417697, 266106, 312987, -1578543, 3635615, -6157911, 8155892, -7689028, 1502546, 14707881, -44539735, 87849728, -136927058, 171008704 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = (-1)^n * n^2, g(n) = -1.

LINKS

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

MATHEMATICA

m = 37; CoefficientList[Series[Product[1/(1+x^k)^((-1)^k*k^2), {k, 1, m}], {x, 0, m}], x] (* Amiram Eldar, May 14 2021 *)

nmax = 40; CoefficientList[Series[Product[(1 + x^(2*k - 1))^((2*k - 1)^2)/(1 + x^(2*k))^(4*k^2), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 14 2021 *)

PROG

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

CROSSREFS

Product_{k>=1} 1/(1+x^k)^((-1)^k*k^b): A029838 (b=0), A284467 (b=1), this sequence (b=2).

Cf. A177155, A307462.

Sequence in context: A299420 A019836 A020503 * A266964 A258197 A255698

Adjacent sequences:  A307481 A307482 A307483 * A307485 A307486 A307487

KEYWORD

sign

AUTHOR

Seiichi Manyama, Apr 10 2019

STATUS

approved

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Last modified September 20 10:51 EDT 2021. Contains 347584 sequences. (Running on oeis4.)