A341371 - OEIS

%I #8 Feb 10 2021 11:11:15

%S 1,20,220,1750,11220,61424,297485,1305260,5276930,19905700,70742012,

%T 238662710,769055130,2378885080,7093202060,20459149350,57254003225,

%U 155851688980,413590326020,1072076963640,2719067915088,6757856447720,16480738170760,39486206985530,93043172921735

%N Expansion of (1 / theta_4(x) - 1)^10 / 1024.

%H Alois P. Heinz, <a href="/A341371/b341371.txt">Table of n, a(n) for n = 10..10000</a>

%F G.f.: (1/1024) * (-1 + Product_{k>=1} (1 + x^k) / (1 - x^k))^10.

%p g:= proc(n, i) option remember; `if`(n=0, 1/2, `if`(i=1, 0,

%p       g(n, i-1))+add(2*g(n-i*j, i-1), j=`if`(i=1, n, 1)..n/i))

%p     end:

%p b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0,

%p       g(n$2)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))

%p     end:

%p a:= n-> b(n, 10):

%p seq(a(n), n=10..34);  # _Alois P. Heinz_, Feb 10 2021

%t nmax = 34; CoefficientList[Series[(1/EllipticTheta[4, 0, x] - 1)^10/1024, {x, 0, nmax}], x] // Drop[#, 10] &

%t nmax = 34; CoefficientList[Series[(1/1024) (-1 + Product[(1 + x^k)/(1 - x^k), {k, 1, nmax}])^10, {x, 0, nmax}], x] // Drop[#, 10] &

%Y Cf. A002448, A004411, A014968, A015128, A327388, A338223, A340947, A341236, A341364, A341365, A341366, A341367, A341368, A341369, A341370.

%K nonn

%O 10,2

%A _Ilya Gutkovskiy_, Feb 10 2021