BBC Russian

A366396

Number of labeled directed graphs on [n] with self loops allowed such that the following implication holds for all x,y in [n]. If x and y are in distinct strongly connected components and y is reachable from x then there is a directed edge from x to y.

1, 2, 16, 368, 34624, 19194752, 47730489856, 452968293106688, 16282682505688059904, 2253889950034687424110592, 1219139359408849690950674415616, 2601990460616856808147727573494857728, 22041041736721298233193355574294486210576384

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..12.

FORMULA

E.g.f.: p(s(2x)-1) where p(x) is the e.g.f. for A001025 and s(x) is the e.g.f. for A003030.

MATHEMATICA

nn = 12; posets = Select[Import["https://oeis.org/A001035/b001035.txt", "Table"],

Length@# == 2 &][[All, 2]]; p[x_] := Total[posets Table[x^i/i!, {i, 0, 18}]]; strong = Select[Import["https://oeis.org/A003030/b003030.txt", "Table"],

Length@# == 2 &][[All, 2]]; s[x_] := Total[Prepend[strong Table[x^i/i!, {i, 1, 58}], 1]]; Table[n!, {n, 0, nn}] CoefficientList[Series[p[s[2 x] - 1], {x, 0, nn}], x]

CROSSREFS

Cf. A366350, A001035, A003030.

Sequence in context: A289972 A179472 A009341 * A015201 A227406 A068471

Adjacent sequences: A366393 A366394 A366395 * A366397 A366398 A366399

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Oct 08 2023

STATUS

approved