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A307526
Expansion of 1/theta_4(1/theta_4(x) - 1), where theta_4() is the Jacobi theta function.
0
1, 4, 24, 144, 828, 4624, 25296, 136192, 723160, 3792564, 19672240, 101054512, 514643952, 2600665872, 13049557280, 65057605120, 322413671228, 1589046496704, 7791836790504, 38025622117168, 184749163375664, 893881787650016, 4308024769339344, 20685919693884672
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Jacobi Theta Functions
FORMULA
G.f.: g(g(x) - 1), where g(x) = g.f. of A015128.
MATHEMATICA
nmax = 23; CoefficientList[Series[1/EllipticTheta[4, 0, 1/EllipticTheta[4, 0, x] - 1], {x, 0, nmax}], x]
g[x_] := g[x] = Product[(1 + x^k)/(1 - x^k), {k, 1, 23}]; a[n_] := a[n] = SeriesCoefficient[g[g[x] - 1], {x, 0, n}]; Table[a[n], {n, 0, 23}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 12 2019
STATUS
approved