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%I #6 Sep 14 2018 14:29:23
%S 1,1,4,36,416,6000,106542,2242093,54399424,1495318752,45938780750,
%T 1559858659359,58007497143180,2344682328265823,102352889947823998,
%U 4798930456964580045,240518006611511552896,12832137350594892322464,726108032647676403262710,43434461707962856186584307
%N a(n) = n! * [x^n] Product_{k>=1} (1 + x^k/k!)^n.
%F a(n) = n! * [x^n] exp(n*Sum_{k>=1} Sum_{j>=1} (-1)^(k+1)*x^(j*k)/(k*(j!)^k)).
%t Table[n! SeriesCoefficient[Product[(1 + x^k/k!)^n, {k, 1, n}], {x, 0, n}], {n, 0, 19}]
%t Table[n! SeriesCoefficient[Exp[n Sum[Sum[(-1)^(k + 1) x^(j k)/(k (j!)^k), {j, 1, n}], {k, 1, n}]], {x, 0, n}], {n, 0, 19}]
%Y Cf. A007837, A032312, A032314, A032315, A319174, A319177.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 12 2018
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