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A285927
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Expansion of (Product_{k>0} (1 - x^(3*k)) / (1 - x^k))^3 in powers of x.
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5
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1, 3, 9, 19, 42, 81, 155, 276, 486, 821, 1368, 2214, 3541, 5544, 8586, 13082, 19740, 29403, 43414, 63423, 91935, 132075, 188418, 266733, 375232, 524331, 728514, 1006216, 1382604, 1889739, 2570719, 3480420, 4691682, 6297102, 8418252, 11209347, 14870970
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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(0) = 1, a(n) = (3/n)*Sum_{k=1..n} A046913(k)*a(n-k) for n > 0.
a(n) ~ exp(2*Pi*sqrt(n/3)) / (2 * 3^(7/4) * n^(3/4)). - Vaclav Kotesovec, Apr 30 2017
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MATHEMATICA
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nmax = 40; CoefficientList[Series[Product[((1 - x^(3*k)) / (1 - x^k))^3, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 30 2017 *)
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CROSSREFS
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(Product_{k>0} (1 - x^(m*k)) / (1 - x^k))^m: A022567 (m=2), this sequence (m=3), A093160 (m=4), A285928 (m=5).
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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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