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%I #11 Aug 03 2021 21:36:18
%S 1,5,2430,5597643,35618229364,483040313859705,11977437107679230274,
%T 490630568583958198181583,30889771581097736768046865352,
%U 2832037863467651034046820871428061,362579939205426756198837321528946171110,62687814132880422794200073791149602981717667
%N a(n) = Bell(3*n,n).
%C 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)))).
%H Alois P. Heinz, <a href="/A346655/b346655.txt">Table of n, a(n) for n = 0..137</a>
%F a(n) ~ (3*n/LambertW(3))^(3*n) / (sqrt(1 + LambertW(3)) * exp(n*(4 - 3/LambertW(3)))).
%F a(n) = A189233(3n,n) = A292860(3n,n). - _Alois P. Heinz_, Jul 27 2021
%p b:= proc(n, k) option remember; `if`(n=0, 1,
%p (1+add(binomial(n-1, j-1)*b(n-j, k), j=1..n-1))*k)
%p end:
%p a:= n-> b(3*n, n):
%p seq(a(n), n=0..11); # _Alois P. Heinz_, Jul 27 2021
%t Table[BellB[3*n, n], {n, 0, 15}]
%Y Cf. A000110, A189233, A242817, A292860, A346654.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Jul 27 2021
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