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%I #4 May 18 2018 19:48:06
%S 1,2,5,19,49,126,469,1177,2881,6481,23101,53725,127153,274288,581925,
%T 1860751,4155649,9279791,19409221,39839239,77052401,229393207,
%U 481747949,1035561408,2082441025,4153434376,7822058869,14686515649,39394280689,79657493191,163600884901
%N a(n) = [x^n] (1/(1 - x))*Product_{k>=1} (1 + n*x^k).
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = [x^n] (1/(1 - x))*exp(Sum_{k>=1} (-1)^(k+1)*n^k*x^k/(k*(1 - x^k))).
%F a(n) = Sum_{j=0..n} A286957(j,n).
%t Table[SeriesCoefficient[1/(1 - x) Product[(1 + n x^k), {k, 1, n}], {x, 0, n}], {n, 0, 30}]
%t Table[SeriesCoefficient[1/(1 - x) Exp[Sum[(-1)^(k + 1) n^k x^k/(k (1 - x^k)), {k, 1, n}]], {x, 0, n}], {n, 0, 30}]
%t Table[SeriesCoefficient[QPochhammer[-n, x]/((1 + n) (1 - x)), {x, 0, n}], {n, 0, 30}]
%Y Cf. A286957, A291698, A303070, A303071, A303914.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, May 18 2018