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%I #7 Sep 14 2018 14:29:21
%S 1,1,8,93,1532,32240,829284,25192454,882825936,35055329832,
%T 1555548490560,76285107738312,4097094075364608,239167754501235456,
%U 15077741379436233120,1020918130521930465120,73892194568147257761024,5693112248722998479169408,465208700406183224884224000
%N a(n) = n! * [x^n] Product_{k>=1} 1/(1 - x^k/k)^n.
%F a(n) = n! * [x^n] exp(n*Sum_{k>=1} Sum_{j>=1} x^(j*k)/(k*j^k)).
%t Table[n! SeriesCoefficient[Product[1/(1 - x^k/k)^n, {k, 1, n}], {x, 0, n}], {n, 0, 18}]
%t Table[n! SeriesCoefficient[Exp[n Sum[Sum[x^(j k)/(k j^k), {j, 1, n}], {k, 1, n}]], {x, 0, n}], {n, 0, 18}]
%Y Cf. A007841, A294469, A299034, A319174, A319177.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 12 2018
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