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A070906 Every third Bell number A000110. 3
1, 5, 203, 21147, 4213597, 1382958545, 682076806159, 474869816156751, 445958869294805289, 545717047936059989389, 846749014511809332450147, 1629595892846007606764728147, 3819714729894818339975525681317 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..12.

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-Fran├žois 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

A070906_list = list(islice(A070906_gen(), 30)) # Chai Wah Wu, Jun 22 2022

CROSSREFS

Cf. A000110, A020557.

Sequence in context: A216615 A215923 A208468 * A208052 A137736 A157389

Adjacent sequences:  A070903 A070904 A070905 * A070907 A070908 A070909

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, May 19 2002

STATUS

approved

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Last modified August 11 12:12 EDT 2022. Contains 356065 sequences. (Running on oeis4.)