%I #12 Jan 12 2021 21:30:08

%S 1,0,2,4,57,348,5235,57930,1037540,16842496,363889755,7792175070,

%T 201054289293,5345844537876,162234861271288,5156725529935952,

%U 181284205622239755,6713109719185427600,269652617328843102055,11418447984579685481310,517839485352765454438270

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

%D G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

%H Andrew Howroyd, <a href="/A098626/b098626.txt">Table of n, a(n) for n = 0..200</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 A000166. - _Andrew Howroyd_, Jan 12 2021

%o (PARI) \\ R(n) is A000166 as e.g.f.; EnrichedGdlSeq defined in A098622.

%o R(n)={exp(-x + O(x*x^n))/(1-x)}

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

%Y Cf. A000166, A014507, A098622, A098624, A098625, A098627.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Oct 26 2004

%E Terms a(14) and beyond from _Andrew Howroyd_, Jan 12 2021