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A319671
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a(n) = [x^n] Product_{k>=2} (1 + x^k)^n.
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3
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1, 0, 2, 3, 10, 30, 77, 252, 682, 2145, 6182, 18887, 56317, 170534, 515930, 1563843, 4759338, 14480073, 44203595, 134972504, 412984510, 1264601502, 3877302717, 11898761051, 36548512477, 112358685555, 345673541514, 1064250223230, 3278695047218, 10107173174013, 31174889414807
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OFFSET
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0,3
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COMMENTS
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Number of partitions of n into distinct parts > 1, with n types of each part.
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LINKS
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FORMULA
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a(n) = [x^n] exp(n*Sum_{k>=1} (A000593(k) + (-1)^k)*x^k/k).
a(n) ~ c * d^n / sqrt(n), where d = 3.136240011804974455586379053639831470878466... and c = 0.220695581251514154138820799337758703024... - Vaclav Kotesovec, Oct 06 2018
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MATHEMATICA
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Table[SeriesCoefficient[Product[(1 + x^k)^n, {k, 2, n}], {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[1/((1 + x) QPochhammer[x, x^2])^n, {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[Exp[n Sum[(Sum[Mod[d, 2] d, {d, Divisors[k]}] + (-1)^k) x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 30}]
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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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