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

Author

William C. Laursen, Dec 03 2020

Keywords

• nonn
• frac

Crossrefs

Cf. A242817, A339402 (denominators).

Programs

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)/A339402(n) = A242817(n)/n!. - Pontus von Brömssen, Dec 03 2020

a(n) = numerator([x^n] exp(n*(exp(x)-1))). - Alois P. Heinz, Dec 07 2020