A346655 a(n) = Bell(3*n,n).

1, 5, 2430, 5597643, 35618229364, 483040313859705, 11977437107679230274, 490630568583958198181583, 30889771581097736768046865352, 2832037863467651034046820871428061, 362579939205426756198837321528946171110, 62687814132880422794200073791149602981717667

Offset: 0

Author

Vaclav Kotesovec, Jul 27 2021

Keywords

• nonn

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

Crossrefs

Cf. A000110, A189233, A242817, A292860, A346654.

Programs

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}]

Formula

a(n) ~ (3*n/LambertW(3))^(3*n) / (sqrt(1 + LambertW(3)) * exp(n*(4 - 3/LambertW(3)))).

a(n) = A189233(3n,n) = A292860(3n,n). - Alois P. Heinz, Jul 27 2021