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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A070906 Every third Bell number A000110. 3

%I #26 Jun 22 2022 14:44:43

%S 1,5,203,21147,4213597,1382958545,682076806159,474869816156751,

%T 445958869294805289,545717047936059989389,846749014511809332450147,

%U 1629595892846007606764728147,3819714729894818339975525681317

%N Every third Bell number A000110.

%F a(n) = Bell(3*n) = A000110(3*n). - _Vladeta Jovovic_, Feb 02 2003

%F a(n) = exp(-1)*Sum_{k>=0} k^(3n)/k!.

%F 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 E.g.f.: exp(-1)*Sum_{n>=0} exp(n^3*x)/n!. - _Vladeta Jovovic_, Aug 24 2006

%t Table[ BellB[3*n], {n, 0, 12}] (* _Jean-François Alcover_, Dec 13 2012 *)

%t BellB[3*Range[0,15]] (* _Harvey P. Dale_, Apr 19 2020 *)

%o (PARI) for(n=0,50,print1(round(sum(i=0,1000,i^(3*n)/(i)!)/exp(1)),","))

%o (Sage) [bell_number(3*n) for n in range(0, 13)] # _Zerinvary Lajos_, May 14 2009

%o (Python)

%o from itertools import accumulate, islice

%o def A070906_gen(): # generator of terms

%o yield 1

%o blist, b = (1,), 1

%o while True:

%o for _ in range(3):

%o blist = list(accumulate(blist, initial=(b:=blist[-1])))

%o yield b

%o A070906_list = list(islice(A070906_gen(),30)) # _Chai Wah Wu_, Jun 22 2022

%Y Cf. A000110, A020557.

%K easy,nonn

%O 0,2

%A _Benoit Cloitre_, May 19 2002

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)