A099710 - OEIS

%I #12 Jan 12 2021 21:32:11

%S 1,2,21,372,9503,323528,13976119,740471952,46918236113,3486842393336,

%T 299252510858253,29285226572514608,3233515108614711055,

%U 399237909648934968160,54699907257463871118015,8261287679602024304387776,1367355850924129919137226337,246745297507913180076213875232

%N Consider the family of directed multigraphs enriched by the species of endofunctions. 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="/A099710/b099710.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 A000312. - _Andrew Howroyd_, Jan 12 2021

%o (PARI) \\ R(n) is A000312 as e.g.f.; EnrichedGdlSeq defined in A098622.

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

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

%Y Cf. A000312, A014507, A098622, A099708, A099709, A099711.

%K nonn

%O 0,2

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

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