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 A014507 Number of digraphs with loops, having unlabeled (non-isolated) nodes and n labeled edges. 19
 1, 2, 13, 162, 3075, 80978, 2784067, 119971162, 6289972169, 392257225754, 28582571639293, 2398695602082442, 229094801646110203, 24652935339990534970, 2963620352166634246995, 395067805289398293647026, 58025593661340099613984593, 9336949406574071339557552946 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. LINKS Muniru A Asiru, Table of n, a(n) for n = 0..50 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} Stirling1(n, k)*Bell(2*k). - Vladeta Jovovic, Jun 21 2003 E.g.f.: exp(-1)*Sum_{n>=0} (1+x)^(n^2)/n!. - Paul D. Hanna, Jul 03 2011 a(n) = n!*exp(-1)*Sum_{k>=sqrt(n)} binomial(k^2,n)/k!. - Paul D. Hanna, Jul 03 2011 MAPLE A014507 := proc(n) add(combinat[stirling1](n, k)*combinat[bell](2*k), k=0..n) ; end proc: seq(A014507(n), n=0..10) ; # R. J. Mathar, Apr 30 2017 MATHEMATICA a[n_] := Sum[StirlingS1[n, k]*BellB[2*k], {k, 0, n}]; Table[a[n], {n, 0, 14}] (* Jean-François Alcover, Jan 21 2018, from Vladeta Jovovic's formula *) PROG (PARI) /* From Vladeta Jovovic's formula: */ {Stirling1(n, k)=n!*polcoeff(binomial(x, n), k)} {Bell(n)=n!*polcoeff(exp(exp(x+x*O(x^n))-1), n)} {a(n)=sum(k=0, n, Stirling1(n, k)*Bell(2*k))} CROSSREFS Cf. A000110 (Bell), A211250, A211251, A211252. Sequence in context: A347051 A291140 A192563 * A132614 A187927 A252766 Adjacent sequences: A014504 A014505 A014506 * A014508 A014509 A014510 KEYWORD nonn AUTHOR Simon Plouffe, Gilbert Labelle (gilbert(AT)lacim.uqam.ca) STATUS approved

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Last modified September 16 23:59 EDT 2024. Contains 375984 sequences. (Running on oeis4.)