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A341366 Expansion of (1 / theta_4(x) - 1)^5 / 32.

%I A341366 #6 Feb 10 2021 09:33:34
%S A341366 1,10,60,275,1060,3612,11210,32310,87665,226130,558684,1329720,
%T A341366 3062905,6853310,14941330,31820642,66343150,135659570,272496680,
%U A341366 538427720,1047788137,2010303890,3806292130,7118038360,13157217715,24055170690,43527162380,77994164515,138463246700
%N A341366 Expansion of (1 / theta_4(x) - 1)^5 / 32.
%F A341366 G.f.: (1/32) * (-1 + Product_{k>=1} (1 + x^k) / (1 - x^k))^5.
%p A341366 g:= proc(n, i) option remember; `if`(n=0, 1/2, `if`(i=1, 0,
%p A341366       g(n, i-1))+add(2*g(n-i*j, i-1), j=`if`(i=1, n, 1)..n/i))
%p A341366     end:
%p A341366 b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0,
%p A341366       g(n$2)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
%p A341366     end:
%p A341366 a:= n-> b(n, 5):
%p A341366 seq(a(n), n=5..33);  # _Alois P. Heinz_, Feb 10 2021
%t A341366 nmax = 33; CoefficientList[Series[(1/EllipticTheta[4, 0, x] - 1)^5/32, {x, 0, nmax}], x] // Drop[#, 5] &
%t A341366 nmax = 33; CoefficientList[Series[(1/32) (-1 + Product[(1 + x^k)/(1 - x^k), {k, 1, nmax}])^5, {x, 0, nmax}], x] // Drop[#, 5] &
%Y A341366 Cf. A002448, A004406, A014968, A015128, A327383, A338223, A340481, A341223, A341364, A341365, A341367, A341368, A341369, A341370.
%K A341366 nonn
%O A341366 5,2
%A A341366 _Ilya Gutkovskiy_, Feb 10 2021