|
Search: id:A070906
|
|
| |
|
| 1, 5, 203, 21147, 4213597, 1382958545, 682076806159, 474869816156751, 445958869294805289, 545717047936059989389, 846749014511809332450147, 1629595892846007606764728147, 3819714729894818339975525681317
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
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
|
|
PROGRAM
|
(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]
|
|
CROSSREFS
|
Cf. A000110, A020557..
Sequence in context: A128791 A041775 A093976 this_sequence A137736 A157389 A128678
Adjacent sequences: A070903 A070904 A070905 this_sequence A070907 A070908 A070909
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), May 19 2002
|
|
|
Search completed in 0.002 seconds
|
