A339401 - OEIS

%I #32 May 27 2022 15:35:05

%S 1,1,3,19,63,322,44683,941977,4677605,668520163,21622993111,

%T 9759873853,31135480907413,194137920764803,64440211018897379,

%U 3298807094967155971,181322497435007616497,532556590750629416219,665881649529214120845679,2596711638295426703997397,1031081559092352146579024047

%N a(n) = numerator of (1/e)^n * Sum_{k>=0}(n^k*k^n)/(n!*k!).

%F a(n)/A339402(n) = A242817(n)/n!. - _Pontus von Brömssen_, Dec 03 2020

%F a(n) = numerator([x^n] exp(n*(exp(x)-1))). - _Alois P. Heinz_, Dec 07 2020

%p A:= proc(n, k) option remember; `if`(n=0, 1, (1+

%p       add(binomial(n-1, j-1)*A(n-j, k), j=1..n-1))*k)

%p     end:

%p a:= n-> numer(A(n$2)/n!):

%p seq(a(n), n=0..20);  # _Alois P. Heinz_, Dec 07 2020

%t a[n_] := BellB[n, n]/n! // Numerator;

%t Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, May 27 2022 *)

%Y Cf. A242817, A339402 (denominators).

%K nonn,frac

%O 0,3

%A _William C. Laursen_, Dec 03 2020