A319554 Expansion of 1/theta_4(q)^12 in powers of q = exp(Pi i t).

1, 24, 312, 2912, 21816, 139152, 783328, 3986112, 18650424, 81251896, 332798544, 1291339296, 4776117216, 16922753616, 57683178432, 189821722688, 604884735288, 1871370360240, 5633654421720, 16535803556064, 47405095227984, 132942579098368, 365211946954656

Offset: 0

Author

Seiichi Manyama, Sep 22 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

1/theta_4(q)^b: A015128 (b=1), A001934 (b=2), A319552 (b=3), A284286 (b=4), A319553 (b=8), this sequence (b=12).

Cf. A002131, A002448 (theta_4(q)), A004413, A286346.

Programs

PARI

N=99; x='x+O('x^N); Vec(prod(k=1, N, ((1-x^(2*k))/(1-x^k)^2)^12))

Formula

Convolution inverse of A286346.

a(n) = (-1)^n * A004413(n).

a(0) = 1, a(n) = (24/n)*Sum_{k=1..n} A002131(k)*a(n-k) for n > 0.

G.f.: Product_{k>=1} ((1 - x^(2k))/(1 - x^k)^2)^12.