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A061694
Generalized Bell numbers.
3
0, 0, 36, 864, 17500, 351000, 7197169, 151633440, 3275925804, 72315234000, 1625547144199, 37102497859152, 857909644412275, 20059247889751161, 473562712831103536, 11274693857547716640, 270435401233629732940
OFFSET
1,3
LINKS
Vaclav Kotesovec, Recurrence (of order 6)
J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, Extended Bell and Stirling Numbers From Hypergeometric Exponentiation, J. Integer Seqs. Vol. 4 (2001), #01.1.4.
FORMULA
a(n) = 1/6*Sum_{i+j+k=n, i, j, k>0} (n!/(i!*j!*k!))^3. - Vladeta Jovovic, Apr 23 2003
a(n) ~ 3^(3*n+1) / (8*Pi^2*n^2). - Vaclav Kotesovec, Mar 14 2014
Sum_{n>=1} a(n) * x^n / (n!)^3 = (1/6) * ( Sum_{n>=1} x^n / (n!)^3 )^3. - Ilya Gutkovskiy, Mar 04 2021
MATHEMATICA
Table[Sum[Sum[(n!/(i!*j!*(n-i-j)!))^3/6, {i, 1, n-j-1}], {j, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Mar 14 2014 *)
CROSSREFS
Sequence in context: A004360 A238931 A081142 * A264192 A122038 A222926
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 19 2001
EXTENSIONS
More terms from Vladeta Jovovic, Apr 23 2003
STATUS
approved