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%I #7 Sep 14 2018 14:29:30
%S 1,1,8,90,1448,29750,747462,22182741,759504720,29468021238,
%T 1277744462870,61232148035531,3213710056592796,183329936018667035,
%U 11294683874759287030,747379761629288205795,52864744954736491460768,3980505280416276751035270,317877846102688099315299678
%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. A005651, A174661, A319175, A319176.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 12 2018
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