A004412 Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-11).

1, -22, 264, -2288, 15994, -95568, 505648, -2425280, 10721832, -44229350, 171861360, -633713808, 2230733648, -7532979344, 24502989984, -77036477760, 234785552122, -695409096096, 2006117554936, -5647472566736

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000122, A008453.

Programs

Mathematica

nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^11, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 18 2015 *)

PARI

q='q+O('q^99); Vec(((eta(q)*eta(q^4))^2/eta(q^2)^5)^11) \\ Altug Alkan, Sep 20 2018

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 = 11 for this sequence. - Vaclav Kotesovec, Aug 18 2015

From Ilya Gutkovskiy, Sep 20 2018: (Start)

G.f.: 1/theta_3(x)^11, where theta_3() is the Jacobi theta function.

G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^11. (End)