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A299036
a(n) = [x^n] Product_{k=1..n} 1/(1-k!*x).
3
1, 1, 7, 381, 502789, 33572762781, 175123095782787181, 99374457734129265819664221, 8158897372191288496224413025490409437, 124778468912108975502836576328262294089846582756189
OFFSET
0,3
LINKS
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 01 2018
STATUS
approved