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%I #10 Oct 06 2018 08:03:59
%S 1,0,2,3,10,30,77,252,682,2145,6182,18887,56317,170534,515930,1563843,
%T 4759338,14480073,44203595,134972504,412984510,1264601502,3877302717,
%U 11898761051,36548512477,112358685555,345673541514,1064250223230,3278695047218,10107173174013,31174889414807
%N a(n) = [x^n] Product_{k>=2} (1 + x^k)^n.
%C Number of partitions of n into distinct parts > 1, with n types of each part.
%H Vaclav Kotesovec, <a href="/A319671/b319671.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = [x^n] exp(n*Sum_{k>=1} (A000593(k) + (-1)^k)*x^k/k).
%F a(n) ~ c * d^n / sqrt(n), where d = 3.136240011804974455586379053639831470878466... and c = 0.220695581251514154138820799337758703024... - _Vaclav Kotesovec_, Oct 06 2018
%t Table[SeriesCoefficient[Product[(1 + x^k)^n, {k, 2, n}], {x, 0, n}], {n, 0, 30}]
%t Table[SeriesCoefficient[1/((1 + x) QPochhammer[x, x^2])^n, {x, 0, n}], {n, 0, 30}]
%t 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}]
%Y Cf. A000593, A025147, A270913, A298598, A304626, A319670.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 25 2018
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