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A004410
Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-9).
2
1, -18, 180, -1320, 7902, -40824, 188232, -792000, 3088980, -11297546, 39090312, -128849976, 406865880, -1236379320, 3629385936, -10324840512, 28542038238, -76852151280, 201967043260, -518957929080, 1305848905416
OFFSET
0,2
LINKS
FORMULA
a(n) ~ (-1)^n * 243*exp(3*Pi*sqrt(n)) / (32768*n^3). - Vaclav Kotesovec, Aug 18 2015
From Ilya Gutkovskiy, Sep 20 2018: (Start)
G.f.: 1/theta_3(x)^9, where theta_3() is the Jacobi theta function.
G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^9. (End)
MATHEMATICA
nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^9, {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)^9) \\ Altug Alkan, Sep 20 2018
CROSSREFS
Sequence in context: A071910 A121038 A341370 * A140325 A199299 A155669
KEYWORD
sign
STATUS
approved