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A070906
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Every third Bell number A000110.
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3
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1, 5, 203, 21147, 4213597, 1382958545, 682076806159, 474869816156751, 445958869294805289, 545717047936059989389, 846749014511809332450147, 1629595892846007606764728147, 3819714729894818339975525681317
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = exp(-1)*Sum_{k>=0} k^(3n)/k!.
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.
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MATHEMATICA
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PROG
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(PARI) for(n=0, 50, print1(round(sum(i=0, 1000, i^(3*n)/(i)!)/exp(1)), ", "))
(Sage) [bell_number(3*n) for n in range(0, 13)] # Zerinvary Lajos, May 14 2009
(Python)
from itertools import accumulate, islice
def A070906_gen(): # generator of terms
yield 1
blist, b = (1, ), 1
while True:
for _ in range(3):
blist = list(accumulate(blist, initial=(b:=blist[-1])))
yield b
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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