A319177 - OEIS

%I #6 Sep 14 2018 14:29:10

%S 1,1,4,39,500,7990,156684,3640392,97543088,2960758800,100428661440,

%T 3764849536800,154567280328768,6897265807262064,332386213584653760,

%U 17204016957686536320,951852354201532742400,56059949872552858763520,3501729575599545174352896,231227806715994322631352960

%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. A007838, A181541, A300187, A319175, A319176.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Sep 12 2018