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A004416 Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-15). 1
1, -30, 480, -5440, 48930, -371136, 2464320, -14688000, 80001120, -403533790, 1904433984, -8477603520, 35829727680, -144548556480, 559157308800, -2081866609920, 7484792950050, -26057409056640, 88057506412320 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(n) ~ (-1)^n * exp(Pi*sqrt(m*n)) * m^((m+1)/4) / (2^(3*(m+1)/2) * n^((m+3)/4)), set m = 15 for this sequence. - Vaclav Kotesovec, Aug 18 2015

From Ilya Gutkovskiy, Sep 20 2018: (Start)

G.f.: 1/theta_3(x)^15, where theta_3() is the Jacobi theta function.

G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^15. (End)

MATHEMATICA

nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^15, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 18 2015 *)

PROG

(PARI) q='q+O('q^99); Vec(((eta(q)*eta(q^4))^2/eta(q^2)^5)^15) \\ Altug Alkan, Sep 20 2018

CROSSREFS

Cf. A000122, A276287.

Sequence in context: A022594 A321955 A321045 * A125487 A258417 A212473

Adjacent sequences:  A004413 A004414 A004415 * A004417 A004418 A004419

KEYWORD

sign

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 17 13:32 EDT 2021. Contains 348049 sequences. (Running on oeis4.)