%I #15 Jan 12 2021 21:30:41

%S 1,2,13,164,3127,82600,2845775,122820136,6446913953,402413160952,

%T 29343933156485,2464029760993520,235446319553848087,

%U 25346231173047308256,3047931031445529965527,406412844141860523543392,59704680455100785101683457,9608818815170839730520275488

%N Consider the family of directed multigraphs enriched by the species of odd sets. 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="/A098638/b098638.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.: exp(-1)*Sum_{n>=0}(1+sinh(x))^(n^2)/n!. - _Vladeta Jovovic_, Mar 04 2008

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

%o (PARI) \\ EnrichedGdlSeq defined in A098622.

%o EnrichedGdlSeq(sinh(x + O(x*x^20))) \\ _Andrew Howroyd_, Jan 12 2021

%Y Cf. A014507, A098622, A098636, A098637, A098639.

%K nonn

%O 0,2

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

%E Missing a(10) inserted and terms a(13) and beyond from _Andrew Howroyd_, Jan 12 2021