A319176 a(n) = n! * [x^n] Product_{k>=1} 1/(1 - x^k/k)^n.

1, 1, 8, 93, 1532, 32240, 829284, 25192454, 882825936, 35055329832, 1555548490560, 76285107738312, 4097094075364608, 239167754501235456, 15077741379436233120, 1020918130521930465120, 73892194568147257761024, 5693112248722998479169408, 465208700406183224884224000

Offset: 0

Author

Ilya Gutkovskiy, Sep 12 2018

Keywords

• nonn

Crossrefs

Cf. A007841, A294469, A299034, A319174, A319177.

Programs

Mathematica

Table[n! SeriesCoefficient[Product[1/(1 - x^k/k)^n, {k, 1, n}], {x, 0, n}], {n, 0, 18}]
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}]

Formula

a(n) = n! * [x^n] exp(n*Sum_{k>=1} Sum_{j>=1} x^(j*k)/(k*j^k)).