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A020557
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Number of oriented multigraphs on n labeled arcs (with loops).
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18
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1, 2, 15, 203, 4140, 115975, 4213597, 190899322, 10480142147, 682076806159, 51724158235372, 4506715738447323, 445958869294805289, 49631246523618756274, 6160539404599934652455, 846749014511809332450147, 128064670049908713818925644
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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REFERENCES
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G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.
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LINKS
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FORMULA
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E.g.f.: exp(x*(d_z)^2)*(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(ceil(sum(i=0, 1000, i^(2*n)/(i)!)/exp(1)), ", "))
(Sage) [bell_number(2*n) for n in range(0, 17)] # Zerinvary Lajos, May 14 2009
(Python)
from itertools import accumulate, islice
def A020557_gen(): # generator of terms
yield 1
blist, b = (1, ), 1
while True:
for _ in range(2):
blist = list(accumulate(blist, initial=(b:=blist[-1])))
yield b
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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