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A294692
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Expansion of Product_{k>=1} 1 / (1 - x^k)^(k*(3*k + 2)).
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3
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1, 5, 31, 148, 667, 2754, 10823, 40393, 145085, 502780, 1690603, 5530649, 17658430, 55141520, 168751779, 506933980, 1496999360, 4350994324, 12460305177, 35192973824, 98116587875, 270220568883, 735668636567, 1981082952258, 5279879097853, 13933764841202
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ exp(4*Pi*n^(3/4) / (3*5^(1/4)) + 2*Zeta(3) * sqrt(5*n) / Pi^2 - 2*5^(5/4) * Zeta(3)^2 * n^(1/4) / Pi^5 + 200*Zeta(3)^3 / (3*Pi^8) - 3*Zeta(3) / (4*Pi^2) + 1/6) * Pi^(1/6) / (A^2 * 2^(3/2) * 5^(1/6) * n^(2/3)), where A is the Glaisher-Kinkelin constant A074962.
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MAPLE
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N:= 50:
S:= series(mul(1/(1-x^k)^(k*(3*k+2)), k=1..N), x, N+1):
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MATHEMATICA
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nmax = 30; CoefficientList[Series[Product[1/(1-x^k)^(k*(3*k+2)), {k, 1, nmax}], {x, 0, nmax}], x]
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CROSSREFS
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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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