A319177 a(n) = n! * [x^n] Product_{k>=1} (1 + x^k/k)^n.

1, 1, 4, 39, 500, 7990, 156684, 3640392, 97543088, 2960758800, 100428661440, 3764849536800, 154567280328768, 6897265807262064, 332386213584653760, 17204016957686536320, 951852354201532742400, 56059949872552858763520, 3501729575599545174352896, 231227806715994322631352960

Offset

0,3

Links

Table of n, a(n) for 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)).

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}]

Crossrefs

Cf. A007838, A181541, A300187, A319175, A319176.

Sequence in context: A300187 A068187 A307698 * A323323 A300188 A177775

Adjacent sequences: A319174 A319175 A319176 * A319178 A319179 A319180

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 12 2018

Status

approved