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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
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
Sequence in context: A022594 A321955 A321045 * A125487 A258417 A212473
KEYWORD
sign
AUTHOR
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)