OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Seiichi Manyama)
Eric Weisstein's World of Mathematics, Jacobi Theta Functions
FORMULA
Convolution inverse of A320067.
Expansion of Product_{k>0} (eta(q^k)*eta(q^(4*k)))^2 / eta(q^(2*k))^5.
Expansion of Product_{k>0} theta_4(q^(2*k-1))/theta_4(q^(2*k)), where theta_4() is the Jacobi theta function. - Seiichi Manyama, Oct 26 2018
MATHEMATICA
nmax = 50; CoefficientList[Series[1/Product[EllipticTheta[3, 0, x^k], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 05 2018 *)
nmax = 50; CoefficientList[Series[Product[(1 + x^(2*k*j))^2/((1 - x^(k*j))*(1 + x^(k*j))^3), {k, 1, nmax}, {j, 1, Floor[nmax/k] + 1}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 08 2018 *)
PROG
(PARI) m=50; x='x+O('x^m); Vec(prod(k=1, 2*m, prod(j=1, floor(2*m/k)+1, (1 + x^(2*k*j))^2/((1 - x^(k*j))*(1 + x^(k*j))^3) ))) \\ G. C. Greubel, Oct 29 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[(&*[(1 + x^(2*k*j))^2/((1 - x^(k*j))*(1 + x^(k*j))^3): j in [1..(Floor(2*m/k)+1)]]): k in [1..2*m]]))); // G. C. Greubel, Oct 29 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Oct 05 2018
STATUS
approved