OFFSET
0,2
FORMULA
a(n) = Bell(3*n) = A000110(3*n). - Vladeta Jovovic, 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_{n>=0} exp(n^3*x)/n!. - Vladeta Jovovic, Aug 24 2006
MATHEMATICA
Table[ BellB[3*n], {n, 0, 12}] (* Jean-François Alcover, Dec 13 2012 *)
BellB[3*Range[0, 15]] (* Harvey P. Dale, Apr 19 2020 *)
PROG
(PARI) for(n=0, 50, print1(round(sum(i=0, 1000, i^(3*n)/(i)!)/exp(1)), ", "))
(Sage) [bell_number(3*n) for n in range(0, 13)] # Zerinvary Lajos, May 14 2009
(Python)
from itertools import accumulate, islice
def A070906_gen(): # generator of terms
yield 1
blist, b = (1, ), 1
while True:
for _ in range(3):
blist = list(accumulate(blist, initial=(b:=blist[-1])))
yield b
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, May 19 2002
STATUS
approved