OFFSET
0,2
REFERENCES
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.
LINKS
G. Labelle, Counting enriched multigraphs according to the number of their edges (or arcs), Discrete Math., 217 (2000), 237-248.
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n-k)*Stirling1(n, k)*A014507(k). - Vladeta Jovovic, May 02 2004
E.g.f.: Sum(Bell(2*n)*log(1-log(1-x))^n/n!, n=0..infinity). - Vladeta Jovovic, May 02 2004
E.g.f.: exp(-1)*Sum((1-log(1-x))^(n^2)/n!,n=0..infinity). - Vladeta Jovovic, Mar 04 2008
MAPLE
A020565 := proc(n)
add((-1)^(n-k)*combinat[stirling1](n, k)*A014507(k), k=0..n) ;
end proc:
seq(A020565(n), n=0..10) ; # R. J. Mathar, Apr 30 2017
MATHEMATICA
b[n_] := Sum[StirlingS1[n, k]*BellB[2*k], {k, 0, n}];
a[n_] := Sum[(-1)^(n-k)*StirlingS1[n, k]*b[k], {k, 0, n}];
Table[a[n], {n, 0, 16}] (* Jean-François Alcover, Jan 21 2018, after Vladeta Jovovic *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gilbert Labelle (gilbert(AT)lacim.uqam.ca), Simon Plouffe
STATUS
approved