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A341370
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Expansion of (1 / theta_4(x) - 1)^9 / 512.
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8
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1, 18, 180, 1311, 7740, 39204, 176388, 721530, 2728053, 9651056, 32246892, 102515508, 311923386, 912771468, 2579132196, 7060677537, 18781247700, 48660380190, 123061973176, 304351869708, 737293187286, 1752035386188, 4089222211212, 9384936015492, 21201250825554
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OFFSET
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9,2
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LINKS
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FORMULA
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G.f.: (1/512) * (-1 + Product_{k>=1} (1 + x^k) / (1 - x^k))^9.
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MAPLE
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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, 9):
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MATHEMATICA
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nmax = 33; CoefficientList[Series[(1/EllipticTheta[4, 0, x] - 1)^9/512, {x, 0, nmax}], x] // Drop[#, 9] &
nmax = 33; CoefficientList[Series[(1/512) (-1 + Product[(1 + x^k)/(1 - x^k), {k, 1, nmax}])^9, {x, 0, nmax}], x] // Drop[#, 9] &
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CROSSREFS
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Cf. A002448, A004410, A014968, A015128, A327387, A338223, A340946, A341228, A341364, A341365, A341366, A341367, A341368, A341369.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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