A319554 - OEIS

%I #16 Sep 24 2018 10:00:15

%S 1,24,312,2912,21816,139152,783328,3986112,18650424,81251896,

%T 332798544,1291339296,4776117216,16922753616,57683178432,189821722688,

%U 604884735288,1871370360240,5633654421720,16535803556064,47405095227984,132942579098368,365211946954656

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

%H Seiichi Manyama, <a href="/A319554/b319554.txt">Table of n, a(n) for n = 0..10000</a>

%F Convolution inverse of A286346.

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

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

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

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

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

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

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 22 2018