VOOZH about

URL: https://oeis.org/A020557

⇱ A020557 - OEIS

login
A020557
Number of oriented multigraphs on n labeled arcs (with loops).
18
1, 2, 15, 203, 4140, 115975, 4213597, 190899322, 10480142147, 682076806159, 51724158235372, 4506715738447323, 445958869294805289, 49631246523618756274, 6160539404599934652455, 846749014511809332450147, 128064670049908713818925644
OFFSET
0,2
REFERENCES
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.
LINKS
Elizabeth Banjo, Representation theory of algebras related to the partition algebra, Unpublished Doctoral thesis, City University London, 2013.
Laura Colmenarejo, Rosa Orellana, Franco Saliola, Anne Schilling, and Mike Zabrocki, An insertion algorithm on multiset partitions with applications to diagram algebras, arXiv:1905.02071 [math.CO], 2019.
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]
FORMULA
a(n) = Bell(2*n) = A000110(2*n). - Vladeta Jovovic, Feb 02 2003
a(n) = exp(-1)*Sum_{k>=0} k^(2n)/k!. - Benoit Cloitre, May 19 2002
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.
E.g.f.: exp(-1)*Sum_{n>=0}exp(n^2*x)/n!. - Vladeta Jovovic, Aug 24 2006
MATHEMATICA
BellB[2 Range[0, 20]] (* Harvey P. Dale, Jul 03 2021 *)
PROG
(PARI) for(n=0, 50, print1(ceil(sum(i=0, 1000, i^(2*n)/(i)!)/exp(1)), ", "))
(SageMath) [bell_number(2*n) for n in range(0, 17)] # Zerinvary Lajos, May 14 2009
(Magma) [Bell(2*n): n in [0..20]]; // Vincenzo Librandi, Feb 05 2017
(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
A020557_list = list(islice(A020557_gen(), 30)) # Chai Wah Wu, Jun 22 2022
CROSSREFS
Cf. A070906. Bisection of Bell numbers A000110.
Cf. A099977.
Sequence in context: A351920 A319466 A379846 * A323118 A184361 A351501
KEYWORD
nonn
AUTHOR
Gilbert Labelle (gilbert(AT)lacim.uqam.ca), Simon Plouffe
STATUS
approved