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.
Original entry on oeis.org
1, 2, 16, 368, 34624, 19194752, 47730489856, 452968293106688, 16282682505688059904, 2253889950034687424110592, 1219139359408849690950674415616, 2601990460616856808147727573494857728, 22041041736721298233193355574294486210576384
Offset: 0
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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]
A369397
Number of binary relations R on [n] such that the (unique) idempotent in {R,R^2,R^3,...} is an equivalence relation.
Original entry on oeis.org
1, 1, 5, 157, 26345, 18218521, 47136254765, 451286947588597, 16264532016440908625, 2253156851039460378774961, 1219026648017155982267265596885, 2601923405098893502520360223043594957, 22040885615442635622424409144799379027505465
Offset: 0
- 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.
- S. Schwarz, On the semigroup of binary relations on a finite set , Czechoslovak Mathematical Journal, 1970.
Cf.
A366866 (binary relations R on [n] such that the (unique) idempotent in {R,R^2,R^3,...} is a quasiorder),
A365534,
A366218,
A365590,
A355612,
A365593,
A366252,
A366350,
A366218.
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nn = 12; strong =Select[Import["https://oeis.org/A003030/b003030.txt", "Table"],
Length@# == 2 &][[All, 2]]; s[x_] := Total[strong Table[x^i/i!, {i, 1, 58}]];
Table[n!, {n, 0, nn}] CoefficientList[Series[Exp [s[2 x] - x], {x, 0, nn}], x]
Showing 1-2 of 2 results.
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