A004413 Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-12).

1, -24, 312, -2912, 21816, -139152, 783328, -3986112, 18650424, -81251896, 332798544, -1291339296, 4776117216, -16922753616, 57683178432, -189821722688, 604884735288, -1871370360240, 5633654421720

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 = 12 for this sequence. - Vaclav Kotesovec, Aug 18 2015

From Ilya Gutkovskiy, Sep 20 2018: (Start)

G.f.: 1/theta_3(x)^12, where theta_3() is the Jacobi theta function.

G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^12. (End)

Mathematica

nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^12, {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)^12) \\ Altug Alkan, Sep 20 2018

Crossrefs

Cf. A000122, A000145.

Sequence in context: A168303 A053215 A290939 * A319554 A069779 A288507

Adjacent sequences: A004410 A004411 A004412 * A004414 A004415 A004416

Keyword

sign

Author

N. J. A. Sloane

Status

approved