A004417 Expansion of (Sum x^(n^2), n = -inf .. inf )^(-16).

1, -32, 544, -6528, 61984, -495040, 3453312, -21581568, 123040288, -648624288, 3194776000, -14823993472, 65231647104, -273714726080, 1100198199040, -4252621927680, 15859616674336, -57229459033664

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 = 16 for this sequence. - Vaclav Kotesovec, Aug 18 2015

From Ilya Gutkovskiy, Sep 20 2018: (Start)

G.f.: 1/theta_3(x)^16, where theta_3() is the Jacobi theta function.

G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^16. (End)

Mathematica

nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^16, {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)^16) \\ Altug Alkan, Sep 20 2018

Crossrefs

Cf. A000122, A000152.

Sequence in context: A022596 A130609 A154306 * A283688 A233683 A093751

Adjacent sequences: A004414 A004415 A004416 * A004418 A004419 A004420

Keyword

sign

Author

N. J. A. Sloane

Status

approved