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A350790 Number of digraphs on n labeled nodes with a global source and sink.

%I A350790 #28 Apr 18 2023 07:37:36
%S A350790 1,2,12,432,64240,33904800,61721081184,394586260943616,
%T A350790 9146766152111641344,792073976107698469670400,
%U A350790 261895415169919230764987845120,335402460348866803020064114666616832,1678893205649791601327398844631544110815232
%N A350790 Number of digraphs on n labeled nodes with a global source and sink.
%C A350790 This sequence differs from A049524 in that the source and sink are restricted to being single nodes.
%H A350790 Andrew Howroyd, <a href="/A350790/b350790.txt">Table of n, a(n) for n = 1..50</a>
%H A350790 R. W. Robinson, <a href="http://cobweb.cs.uga.edu/~rwr/publications/components.pdf">Counting digraphs with restrictions on the strong components</a>, Combinatorics and Graph Theory '95 (T.-H. Ku, ed.), World Scientific, Singapore (1995), 343-354.
%F A350790 For n >= 3, a(n) = 2*n*(n-1)*A003030(n-1) (Robinson equation 22). - _Geoffrey Critzer_, Apr 17 2023
%t A350790 nn = 15; strong = Select[Import["https://oeis.org/A003030/b003030.txt", "Table"],
%t A350790    Length@# == 2 &][[All, 2]]; s[z_] := Total[strong Table[z^i/i!, {i, 1, 58}]];
%t A350790 ggf[egf_] := Normal[Series[egf, {z, 0, nn}]] /. Table[z^i -> z^i/2^Binomial[i, 2], {i, 1, nn + 1}];egf[ggf_] := Normal[Series[ggf, {z, 0, nn}]] /.Table[z^i -> z^i*2^Binomial[i, 2], {i, 1, nn + 1}];Table[n!, {n, 0, nn}] CoefficientList[
%t A350790 Series[z - z^2 + Exp[(u - 1) (v - 1) s[ z]] egf[ggf[z Exp[(u - 1) s[z]]]*1/ggf[Exp[-s[z]]]*ggf[z Exp[(v - 1) s[ z]]]] /. {u -> 0, v -> 0}, {z, 0, nn}], z] (* _Geoffrey Critzer_, Apr 17 2023 *)
%o A350790 (PARI) InitFinallyV(12) \\ See A350791 for program code.
%Y A350790 The unlabeled version is A350794.
%Y A350790 Row sums of A350791.
%Y A350790 Cf. A049524, A165950, A350792, A003030.
%K A350790 nonn
%O A350790 1,2
%A A350790 _Andrew Howroyd_, Jan 16 2022