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 A341366 Expansion of (1 / theta_4(x) - 1)^5 / 32. 7
 1, 10, 60, 275, 1060, 3612, 11210, 32310, 87665, 226130, 558684, 1329720, 3062905, 6853310, 14941330, 31820642, 66343150, 135659570, 272496680, 538427720, 1047788137, 2010303890, 3806292130, 7118038360, 13157217715, 24055170690, 43527162380, 77994164515, 138463246700 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,2 LINKS Table of n, a(n) for n=5..33. FORMULA G.f.: (1/32) * (-1 + Product_{k>=1} (1 + x^k) / (1 - x^k))^5. 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, 5): seq(a(n), n=5..33); # Alois P. Heinz, Feb 10 2021 MATHEMATICA nmax = 33; CoefficientList[Series[(1/EllipticTheta[4, 0, x] - 1)^5/32, {x, 0, nmax}], x] // Drop[#, 5] & nmax = 33; CoefficientList[Series[(1/32) (-1 + Product[(1 + x^k)/(1 - x^k), {k, 1, nmax}])^5, {x, 0, nmax}], x] // Drop[#, 5] & CROSSREFS Cf. A002448, A004406, A014968, A015128, A327383, A338223, A340481, A341223, A341364, A341365, A341367, A341368, A341369, A341370. Sequence in context: A228581 A241929 A278721 * A004406 A003472 A112502 Adjacent sequences: A341363 A341364 A341365 * A341367 A341368 A341369 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Feb 10 2021 STATUS approved

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Last modified May 20 02:39 EDT 2024. Contains 372703 sequences. (Running on oeis4.)