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A004417 Expansion of (Sum x^(n^2), n = -inf .. inf )^(-16). 1
1, -32, 544, -6528, 61984, -495040, 3453312, -21581568, 123040288, -648624288, 3194776000, -14823993472, 65231647104, -273714726080, 1100198199040, -4252621927680, 15859616674336, -57229459033664 (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 = 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

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Last modified September 27 21:12 EDT 2021. Contains 347698 sequences. (Running on oeis4.)