A299036 a(n) = [x^n] Product_{k=1..n} 1/(1-k!*x).

1, 1, 7, 381, 502789, 33572762781, 175123095782787181, 99374457734129265819664221, 8158897372191288496224413025490409437, 124778468912108975502836576328262294089846582756189

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..30

Formula

From Vaclav Kotesovec, Feb 02 2018: (Start)

a(n) ~ (n!)^n.

a(n) ~ 2^(n/2) * Pi^(n/2) * n^(n*(2*n+1)/2) / exp(n^2 - 1/12). (End)

Mathematica

Table[SeriesCoefficient[Product[1/(1 - k!*x), {k, 1, n}], {x, 0, n}], {n, 0, 12}] (* Vaclav Kotesovec, Feb 02 2018 *)

Crossrefs

Cf. A000178, A036740.

Cf. A007820, A298851, A299035.

Sequence in context: A232454 A140638 A367868 * A112905 A293459 A058275

Adjacent sequences: A299033 A299034 A299035 * A299037 A299038 A299039

Keyword

nonn

Author

Seiichi Manyama, Feb 01 2018

Status

approved