cp's OEIS Frontend

A070906 Every third Bell number A000110.

%I A070906 #26 Jun 22 2022 14:44:43
%S A070906 1,5,203,21147,4213597,1382958545,682076806159,474869816156751,
%T A070906 445958869294805289,545717047936059989389,846749014511809332450147,
%U A070906 1629595892846007606764728147,3819714729894818339975525681317
%N A070906 Every third Bell number A000110.
%F A070906 a(n) = Bell(3*n) = A000110(3*n). - _Vladeta Jovovic_, Feb 02 2003
%F A070906 a(n) = exp(-1)*Sum_{k>=0} k^(3n)/k!.
%F A070906 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.
%F A070906 E.g.f.: exp(-1)*Sum_{n>=0} exp(n^3*x)/n!. - _Vladeta Jovovic_, Aug 24 2006
%t A070906 Table[ BellB[3*n], {n, 0, 12}] (* _Jean-François Alcover_, Dec 13 2012 *)
%t A070906 BellB[3*Range[0,15]] (* _Harvey P. Dale_, Apr 19 2020 *)
%o A070906 (PARI) for(n=0,50,print1(round(sum(i=0,1000,i^(3*n)/(i)!)/exp(1)),","))
%o A070906 (Sage) [bell_number(3*n) for n in range(0, 13)] # _Zerinvary Lajos_, May 14 2009
%o A070906 (Python)
%o A070906 from itertools import accumulate, islice
%o A070906 def A070906_gen(): # generator of terms
%o A070906     yield 1
%o A070906     blist, b = (1,), 1
%o A070906     while True:
%o A070906         for _ in range(3):
%o A070906             blist = list(accumulate(blist, initial=(b:=blist[-1])))
%o A070906         yield b
%o A070906 A070906_list = list(islice(A070906_gen(),30)) # _Chai Wah Wu_, Jun 22 2022
%Y A070906 Cf. A000110, A020557.
%K A070906 easy,nonn
%O A070906 0,2
%A A070906 _Benoit Cloitre_, May 19 2002