A319174 a(n) = n! * [x^n] Product_{k>=1} 1/(1 - x^k/k!)^n.

1, 1, 8, 90, 1448, 29750, 747462, 22182741, 759504720, 29468021238, 1277744462870, 61232148035531, 3213710056592796, 183329936018667035, 11294683874759287030, 747379761629288205795, 52864744954736491460768, 3980505280416276751035270, 317877846102688099315299678

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

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}]

Crossrefs

Cf. A005651, A174661, A319175, A319176.

Sequence in context: A092956 A345876 A295623 * A034667 A116149 A184709

Adjacent sequences: A319171 A319172 A319173 * A319175 A319176 A319177

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 12 2018

Status

approved