A339401 a(n) = numerator of (1/e)^n * Sum_{k>=0}(n^k*k^n)/(n!*k!).
1, 1, 3, 19, 63, 322, 44683, 941977, 4677605, 668520163, 21622993111, 9759873853, 31135480907413, 194137920764803, 64440211018897379, 3298807094967155971, 181322497435007616497, 532556590750629416219, 665881649529214120845679, 2596711638295426703997397, 1031081559092352146579024047
Offset: 0
Programs
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Maple
A:= proc(n, k) option remember; `if`(n=0, 1, (1+ add(binomial(n-1, j-1)*A(n-j, k), j=1..n-1))*k) end: a:= n-> numer(A(n$2)/n!): seq(a(n), n=0..20); # Alois P. Heinz, Dec 07 2020 -
Mathematica
a[n_] := BellB[n, n]/n! // Numerator; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 27 2022 *)
Formula
a(n) = numerator([x^n] exp(n*(exp(x)-1))). - Alois P. Heinz, Dec 07 2020