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A366350
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 then there is a directed edge from x to y or from y to x.
2
1, 2, 12, 240, 29056, 18656960, 47473519744, 452285200546816, 16275391021965395968, 2253596336074652670148608, 1219094258112479334941371285504, 2601963635581642923807860961645363200
OFFSET
0,2
COMMENTS
Equivalently, a(n) is the number of n x n binary relation matrices such that each of the blocks above the diagonal of its Frobenius normal form is a 1-block (a block containing all 1's). See Gregory, Kirkland and Pullman for definition of Frobenius normal form.
LINKS
D. A. Gregory, S. Kirkland, and N. J. Pullman, Power convergent Boolean matrices, Linear Algebra and its Applications, Volume 179, 15 January 1993, Pages 105-117.
FORMULA
E.g.f.: 1/(1-(s(2x)-1)) where s(x) is the e.g.f. for A003030.
MATHEMATICA
nn = 11; 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[1/(1 - (s[x + x] - 1)), {x, 0, nn}], x]
CROSSREFS
Cf. A003030.
Sequence in context: A132877 A007685 A132987 * A087046 A111403 A325501
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Oct 07 2023
STATUS
approved