The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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