A004411 Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-10).

1, -20, 220, -1760, 11420, -63624, 315040, -1418560, 5903260, -22976820, 84413912, -294841120, 984745120, -3159938760, 9780562880, -29296914112, 85169213340, -240882506920, 664216884540, -1788966694240, 4714033526616, -12170584419840, 30826269009760

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 = 10 for this sequence. - Vaclav Kotesovec, Aug 18 2015

From Ilya Gutkovskiy, Sep 20 2018: (Start)

G.f.: 1/theta_3(x)^10, where theta_3() is the Jacobi theta function.

G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^10. (End)

Mathematica

nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^10, {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)^10) \\ Altug Alkan, Sep 20 2018

Crossrefs

Cf. A000122, A000144.

Sequence in context: A213351 A140236 A341371 * A140354 A155673 A000833

Adjacent sequences: A004408 A004409 A004410 * A004412 A004413 A004414

Keyword

sign

Author

N. J. A. Sloane

Status

approved