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A346654
a(n) = Bell(2*n,n).
3
1, 2, 94, 12351, 3188340, 1362057155, 869725707522, 775929767223352, 921839901090823112, 1406921223577401454239, 2682502220690005671884710, 6248503930824315386034050253, 17460431497766377837983159782652, 57647207262184459310081410522242310, 222006095854149044448961838142906736554
OFFSET
0,2
LINKS
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
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jul 27 2021
STATUS
approved