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A070906
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Every third Bell number A000110.
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3
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1, 5, 203, 21147, 4213597, 1382958545, 682076806159, 474869816156751, 445958869294805289, 545717047936059989389, 846749014511809332450147, 1629595892846007606764728147, 3819714729894818339975525681317
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n) = Bell(3*n) = A000110(3*n). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 02 2003
a(n) = EXP(-1)*sum(k=>0, k^(3n)/k!).
E.g.f.: exp(x*(d_z)^3)*(exp(exp(z)-1)) |_{z=0}, with the derivative operator d_z := d/dz. Adapted from eqs.(14) and (15) of the 1999 C. M. Bender reference given in A000110.
E.g.f.: exp(-1)*Sum(exp(n^3*x)/n!,n=0..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 24 2006
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PROG
| (PARI) for(n=0, 50, print1(round(sum(i=0, 1000, i^(3*n)/(i)!)/exp(1)), ", "))
(Other) sage: [bell_number(3*n) for n in xrange(0, 13)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 14 2009]
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CROSSREFS
| Cf. A000110, A020557..
Sequence in context: A196799 A196587 A197044 * A137736 A157389 A128678
Adjacent sequences: A070903 A070904 A070905 * A070907 A070908 A070909
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KEYWORD
| easy,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), May 19 2002
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