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A350790
Number of digraphs on n labeled nodes with a global source and sink.
5
1, 2, 12, 432, 64240, 33904800, 61721081184, 394586260943616, 9146766152111641344, 792073976107698469670400, 261895415169919230764987845120, 335402460348866803020064114666616832, 1678893205649791601327398844631544110815232
OFFSET
1,2
COMMENTS
This sequence differs from A049524 in that the source and sink are restricted to being single nodes.
LINKS
R. W. Robinson, Counting digraphs with restrictions on the strong components, Combinatorics and Graph Theory '95 (T.-H. Ku, ed.), World Scientific, Singapore (1995), 343-354.
FORMULA
For n >= 3, a(n) = 2*n*(n-1)*A003030(n-1) (Robinson equation 22). - Geoffrey Critzer, Apr 17 2023
MATHEMATICA
nn = 15; strong = Select[Import["https://oeis.org/A003030/b003030.txt", "Table"],
Length@# == 2 &][[All, 2]]; s[z_] := Total[strong Table[z^i/i!, {i, 1, 58}]];
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[
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 *)
PROG
(PARI) InitFinallyV(12) \\ See A350791 for program code.
CROSSREFS
The unlabeled version is A350794.
Row sums of A350791.
Sequence in context: A012786 A168504 A062738 * A296623 A009510 A091471
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 16 2022
STATUS
approved