A004408 Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-7).
1, -14, 112, -672, 3346, -14560, 57120, -206208, 694960, -2209774, 6683040, -19345760, 53874912, -144936288, 377965760, -958231680, 2367566866, -5713057728, 13488657168, -31210552800, 70873262880, -158145658560
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..10000
Programs
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Mathematica
nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^7, {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)^7) \\ Altug Alkan, Sep 20 2018
Formula
a(n) ~ (-1)^n * 49*exp(Pi*sqrt(7*n)) / (4096*n^(5/2)). - Vaclav Kotesovec, Aug 18 2015
From Ilya Gutkovskiy, Sep 20 2018: (Start)
G.f.: 1/theta_3(x)^7, where theta_3() is the Jacobi theta function.
G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^7. (End)