A070908 Every fifth Bell number A000110.

1, 52, 115975, 1382958545, 51724158235372, 4638590332229999353, 846749014511809332450147, 281600203019560266563340426570, 157450588391204931289324344702531067

Offset

0,2

Links

Table of n, a(n) for n=0..8.

Formula

a(n) = A000110(5*n).

a(n) = exp(-1)*Sum_{k>=0} k^(5n)/k!.

E.g.f.: exp(x*(d_z)^5)*(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.

Mathematica

BellB[Range[0, 40, 5]] (* Harvey P. Dale, Oct 28 2019 *)

Prog

(PARI) for(n=0, 50, print1(round(sum(i=0, 1000, i^(5*n)/(i)!)/exp(1)), ", "))
(Sage) [bell_number(5*n) for n in range(0, 9)] # Zerinvary Lajos, May 15 2009
(Python)
from itertools import accumulate, islice
def A070908_gen(): # generator of terms
    yield 1
    blist, b = (1, ), 1
    while True:
        for _ in range(5):
            blist = list(accumulate(blist, initial=(b:=blist[-1])))
        yield b
A070908_list = list(islice(A070908_gen(), 20)) # Chai Wah Wu, Jun 22 2022

Crossrefs

Sequence in context: A208464 A211252 A208470 * A198980 A198721 A198912

Adjacent sequences: A070905 A070906 A070907 * A070909 A070910 A070911

Keyword

easy,nonn

Author

Benoit Cloitre, May 19 2002

Status

approved