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a(n) = [x^n] Product_{k>=1} (1 + n*x^k)^k.
5

%I #11 Feb 02 2018 10:09:24

%S 1,1,4,27,80,400,1908,6223,31296,116478,450100,1828915,7360848,

%T 26906828,95776772,403908975,1421758720,5072014447,18481180644,

%U 68350964211,246180936400,827642046294,2958748580084,10294629775620,36607347335232,120800714172500,407951731319860,1405943613730899

%N a(n) = [x^n] Product_{k>=1} (1 + n*x^k)^k.

%H Vaclav Kotesovec, <a href="/A298987/b298987.txt">Table of n, a(n) for n = 0..1000</a>

%t Table[SeriesCoefficient[Product[(1 + n x^k)^k, {k, 1, n}], {x, 0, n}], {n, 0, 27}]

%Y Cf. A026007, A261562, A266857, A266891, A291698, A297322, A298985, A298986, A298988.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jan 31 2018