A346654 a(n) = Bell(2*n,n).

1, 2, 94, 12351, 3188340, 1362057155, 869725707522, 775929767223352, 921839901090823112, 1406921223577401454239, 2682502220690005671884710, 6248503930824315386034050253, 17460431497766377837983159782652, 57647207262184459310081410522242310, 222006095854149044448961838142906736554

Offset: 0

Author

Vaclav Kotesovec, Jul 27 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..198

Crossrefs

Cf. A000110, A189233, A242817, A292860, A346655.

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(2*n, n):
seq(a(n), n=0..14);  # Alois P. Heinz, Jul 27 2021

Mathematica

Table[BellB[2*n, n], {n, 0, 20}]

Formula

a(n) ~ 4^n * exp((2/LambertW(2) - 3)*n) * n^(2*n) / (sqrt(1 + LambertW(2)) * LambertW(2)^(2*n)).

a(n) = A189233(2n,n) = A292860(2n,n). - Alois P. Heinz, Jul 27 2021