A341369 Expansion of (1 / theta_4(x) - 1)^8 / 256.
1, 16, 144, 952, 5136, 23904, 99292, 376512, 1324376, 4372632, 13673888, 40787848, 116713350, 321861312, 858693192, 2223428224, 5602833292, 13772292360, 33089930724, 77846837848, 179602530648, 406914172336, 906438716196, 1987418937952, 4293164981849, 9144987747024
Offset: 8
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 8..10000
Crossrefs
Programs
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Maple
g:= proc(n, i) option remember; `if`(n=0, 1/2, `if`(i=1, 0, g(n, i-1))+add(2*g(n-i*j, i-1), j=`if`(i=1, n, 1)..n/i)) end: b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0, g(n$2)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))) end: a:= n-> b(n, 8): seq(a(n), n=8..33); # Alois P. Heinz, Feb 10 2021 -
Mathematica
nmax = 33; CoefficientList[Series[(1/EllipticTheta[4, 0, x] - 1)^8/256, {x, 0, nmax}], x] // Drop[#, 8] & nmax = 33; CoefficientList[Series[(1/256) (-1 + Product[(1 + x^k)/(1 - x^k), {k, 1, nmax}])^8, {x, 0, nmax}], x] // Drop[#, 8] &
Formula
G.f.: (1/256) * (-1 + Product_{k>=1} (1 + x^k) / (1 - x^k))^8.