A307526 Expansion of 1/theta_4(1/theta_4(x) - 1), where theta_4() is the Jacobi theta function.

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

Table of n, a(n) for n=0..23.

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

Cf. A002448, A015128, A307050, A307127, A307128, A307186.

Sequence in context: A370234 A114169 A121102 * A067411 A045915 A052609

Adjacent sequences: A307523 A307524 A307525 * A307527 A307528 A307529

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 12 2019

Status

approved