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A346655
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a(n) = Bell(3*n,n).
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3
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1, 5, 2430, 5597643, 35618229364, 483040313859705, 11977437107679230274, 490630568583958198181583, 30889771581097736768046865352, 2832037863467651034046820871428061, 362579939205426756198837321528946171110, 62687814132880422794200073791149602981717667
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OFFSET
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0,2
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COMMENTS
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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)))).
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LINKS
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FORMULA
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a(n) ~ (3*n/LambertW(3))^(3*n) / (sqrt(1 + LambertW(3)) * exp(n*(4 - 3/LambertW(3)))).
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MAPLE
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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):
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MATHEMATICA
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Table[BellB[3*n, n], {n, 0, 15}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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