A339402 a(n) = denominator of (1/e)^n * Sum_{k>=0}(n^k*k^n)/(n!*k!).

1, 1, 1, 2, 2, 3, 120, 720, 1008, 40320, 362880, 45360, 39916800, 68428800, 6227020800, 87178291200, 1307674368000, 1046139494400, 355687428096000, 376610217984000, 40548366802944000, 2432902008176640000, 5676771352412160000, 40142883134914560000, 25852016738884976640000

Offset: 0

Author

William C. Laursen, Dec 03 2020

Keywords

• nonn
• frac

Crossrefs

Cf. A339401 for numerators and relation to A242817.

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-> denom(A(n$2)/n!):
seq(a(n), n=0..30);  # Alois P. Heinz, Dec 07 2020

Mathematica

a[n_] := BellB[n, n]/n! // Denominator;
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 27 2022 *)

Formula

A339401(n)/a(n) = A242817(n)/n!. - Pontus von Brömssen, Dec 03 2020

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