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A004417
Expansion of (Sum x^(n^2), n = -inf .. inf )^(-16).
1
1, -32, 544, -6528, 61984, -495040, 3453312, -21581568, 123040288, -648624288, 3194776000, -14823993472, 65231647104, -273714726080, 1100198199040, -4252621927680, 15859616674336, -57229459033664
OFFSET
0,2
LINKS
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 = 16 for this sequence. - Vaclav Kotesovec, Aug 18 2015
From Ilya Gutkovskiy, Sep 20 2018: (Start)
G.f.: 1/theta_3(x)^16, where theta_3() is the Jacobi theta function.
G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^16. (End)
MATHEMATICA
nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^16, {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)^16) \\ Altug Alkan, Sep 20 2018
CROSSREFS
Sequence in context: A022596 A130609 A154306 * A283688 A233683 A093751
KEYWORD
sign
STATUS
approved