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A303071
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a(n) = [x^n] (1/(1 - x))*Product_{k>=1} (1 + x^k)^n.
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3
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1, 2, 6, 23, 90, 362, 1491, 6225, 26242, 111479, 476466, 2046464, 8825559, 38191467, 165751529, 721177328, 3144703234, 13739010855, 60127642329, 263545670385, 1156732481150, 5083320593976, 22364017244278, 98491038664903, 434160710647831, 1915482295831037, 8457663096970431
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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) = [x^n] (1/(1 - x))*exp(n*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k))).
a(n) ~ c * d^n / sqrt(n), where d = A270914 = 4.5024767476173544877385939327007... and c = 0.44252758868364961050787771300805... - Vaclav Kotesovec, May 19 2018
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MATHEMATICA
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Table[SeriesCoefficient[1/(1 - x) Product[(1 + x^k)^n, {k, 1, n}], {x, 0, n}], {n, 0, 26}]
Table[SeriesCoefficient[1/(1 - x) Exp[n Sum[(-1)^(k + 1) x^k/(k (1 - x^k)), {k, 1, n}]], {x, 0, n}], {n, 0, 26}]
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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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