|
|
A070907
|
|
Every fourth Bell number A000110.
|
|
0
|
|
|
1, 15, 4140, 4213597, 10480142147, 51724158235372, 445958869294805289, 6160539404599934652455, 128064670049908713818925644, 3819714729894818339975525681317, 157450588391204931289324344702531067
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|