A070907 Every fourth Bell number A000110.

1, 15, 4140, 4213597, 10480142147, 51724158235372, 445958869294805289, 6160539404599934652455, 128064670049908713818925644, 3819714729894818339975525681317, 157450588391204931289324344702531067

Offset

0,2

Links

Table of n, a(n) for n=0..10.

Formula

a(n) = A000110(4*n).

a(n) = exp(-1)*Sum_{k>=0} k^(4n)/k!.

E.g.f.: exp(x*(d_z)^4)*(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

Table[BellB[4*n], {n, 0, 10}] (* Amiram Eldar, Jun 11 2022 *)

Prog

(PARI) for(n=0, 50, print1(round(sum(i=0, 1000, i^(4*n)/(i)!)/exp(1)), ", "))
(Sage) [bell_number(4*n) for n in range(0, 11)] # Zerinvary Lajos, May 15 2009
(Python)
from itertools import accumulate, islice
def A070907_gen(): # generator of terms
    yield 1
    blist, b = (1, ), 1
    while True:
        for _ in range(4):
            blist = list(accumulate(blist, initial=(b:=blist[-1])))
        yield b
A070907_list = list(islice(A070907_gen(), 20)) # Chai Wah Wu, Jun 22 2022

Crossrefs

Cf. A000110.

Sequence in context: A139297 A211251 A208469 * A208053 A361453 A079919

Adjacent sequences: A070904 A070905 A070906 * A070908 A070909 A070910

Keyword

easy,nonn

Author

Benoit Cloitre, May 19 2002

Status

approved