A004415 Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-14).

1, -28, 420, -4480, 38052, -273336, 1723008, -9770240, 50722980, -244273820, 1102294984, -4698110592, 19034512000, -73696070840, 273868321536, -980502270720, 3392689809572, -11376760267320, 37060195850020

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 = 14 for this sequence. - Vaclav Kotesovec, Aug 18 2015

From Ilya Gutkovskiy, Sep 20 2018: (Start)

G.f.: 1/theta_3(x)^14, where theta_3() is the Jacobi theta function.

G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^14. (End)

Mathematica

nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^14, {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)^14) \\ Altug Alkan, Sep 20 2018

Crossrefs

Cf. A000122, A276286.

Sequence in context: A233333 A271793 A024213 * A096949 A093974 A121803

Adjacent sequences: A004412 A004413 A004414 * A004416 A004417 A004418

Keyword

sign

Author

N. J. A. Sloane

Status

approved