A319175 a(n) = n! * [x^n] Product_{k>=1} (1 + x^k/k!)^n.
1, 1, 4, 36, 416, 6000, 106542, 2242093, 54399424, 1495318752, 45938780750, 1559858659359, 58007497143180, 2344682328265823, 102352889947823998, 4798930456964580045, 240518006611511552896, 12832137350594892322464, 726108032647676403262710, 43434461707962856186584307
Offset: 0
Keywords
Programs
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Mathematica
Table[n! SeriesCoefficient[Product[(1 + x^k/k!)^n, {k, 1, n}], {x, 0, n}], {n, 0, 19}] 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}]
Formula
a(n) = n! * [x^n] exp(n*Sum_{k>=1} Sum_{j>=1} (-1)^(k+1)*x^(j*k)/(k*(j!)^k)).