OFFSET
1,2
COMMENTS
This sequence differs from A049524 in that the source and sink are restricted to being single nodes.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..50
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
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 16 2022
STATUS
approved