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A004408
Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-7).
2
1, -14, 112, -672, 3346, -14560, 57120, -206208, 694960, -2209774, 6683040, -19345760, 53874912, -144936288, 377965760, -958231680, 2367566866, -5713057728, 13488657168, -31210552800, 70873262880, -158145658560
OFFSET
0,2
LINKS
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)
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 *)
PROG
(PARI) q='q+O('q^99); Vec(((eta(q)*eta(q^4))^2/eta(q^2)^5)^7) \\ Altug Alkan, Sep 20 2018
CROSSREFS
Sequence in context: A234800 A213348 A341368 * A002409 A155655 A007817
KEYWORD
sign
STATUS
approved