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%I #12 Jan 12 2021 21:32:02
%S 1,4,84,3568,305712,87782720,144600947392,1139235294403328,
%T 37012349010095737088,4840037457225169875031040,
%U 2535930555678883610642223895552,5317274645187046706095607711946092544,44602319906972740832371696997145322907873280
%N Consider the family of directed multigraphs enriched by the species of directed graphs. 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="/A099706/b099706.txt">Table of n, a(n) for n = 0..50</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 A002416. - _Andrew Howroyd_, Jan 12 2021
%o (PARI) \\ R(n) is A002416 as e.g.f.; EnrichedGdlSeq defined in A098622.
%o R(n)={sum(k=0, n, 2^(k^2)*x^k/k!) + O(x*x^n)}
%o EnrichedGdlSeq(R(15)) \\ _Andrew Howroyd_, Jan 12 2021
%Y Cf. A002416, A014507, A098622, A099704, A099705, A099707.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Oct 26 2004
%E Terms a(10) and beyond from _Andrew Howroyd_, Jan 12 2021
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