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A307522
Expansion of Product_{k>=1} ((1 + x)^k - x^k)/((1 + x)^k + x^k).
2
1, -2, 2, -2, 4, -10, 22, -42, 72, -116, 188, -332, 662, -1432, 3148, -6736, 13784, -26894, 50254, -90782, 160856, -285230, 518170, -983710, 1964800, -4090002, 8705322, -18582722, 39219572, -81148034, 163946630, -323136562, 622125982, -1173528562, 2179230066
OFFSET
0,2
FORMULA
G.f.: theta_4(x/(1 + x)), where theta_4() is the Jacobi theta function.
MATHEMATICA
m = 34; CoefficientList[Series[Product[((1 + x)^k - x^k)/((1 + x)^k + x^k), {k, 1, m}], {x, 0, m}], x] (* Amiram Eldar, May 14 2021 *)
PROG
(PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1+x)^k-x^k)/((1+x)^k+x^k)))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 12 2019
STATUS
approved