OFFSET
0,2
COMMENTS
In general, for k>=1, Bell(k*n,n) ~ (k*n/LambertW(k))^(k*n) / (sqrt(1 + LambertW(k)) * exp(n*(k + 1 - k/LambertW(k)))).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..137
FORMULA
a(n) ~ (3*n/LambertW(3))^(3*n) / (sqrt(1 + LambertW(3)) * exp(n*(4 - 3/LambertW(3)))).
MAPLE
b:= proc(n, k) option remember; `if`(n=0, 1,
(1+add(binomial(n-1, j-1)*b(n-j, k), j=1..n-1))*k)
end:
a:= n-> b(3*n, n):
seq(a(n), n=0..11); # Alois P. Heinz, Jul 27 2021
MATHEMATICA
Table[BellB[3*n, n], {n, 0, 15}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jul 27 2021
STATUS
approved