A099698 - OEIS

%I #9 Jan 12 2021 21:31:23

%S 1,2,17,248,5403,160420,6142567,291996934,16759322733,1136940595762,

%T 89641455771637,8102778995663368,830222723124364047,

%U 95509354134959796556,12236166882713532940611,1733521075683722202738222,269910543278748394820341769,45936441912756036235229989058

%N Consider the family of directed multigraphs enriched by the species of involutions. Sequence gives number of those multigraphs with n labeled loops and arcs.

%H Andrew Howroyd, <a href="/A099698/b099698.txt">Table of n, a(n) for n = 0..100</a>

%H G. Paquin, <a href="/A038205/a038205.pdf">Dénombrement de multigraphes enrichis</a>, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

%F E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014507 and 1 + R(x) is the e.g.f. of A000085. - _Andrew Howroyd_, Jan 12 2021

%o (PARI) \\ R(n) is A000085 as e.g.f.; EnrichedGdlSeq defined in A098622.

%o R(n)={exp(x+x^2/2 + O(x*x^n))}

%o EnrichedGdlSeq(R(20)) \\ _Andrew Howroyd_, Jan 12 2021

%Y Cf. A000085, A014507, A098622, A099696, A099697, A099699.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jun 25 2017

%E Dead sequence restored, corrected and extended by _Andrew Howroyd_, Jan 12 2021