A086366
Number of labeled n-node digraphs in which every node belongs to a directed cycle.
Original entry on oeis.org
1, 0, 1, 18, 1699, 587940, 750744901, 3556390155318, 63740128872703879, 4405426607409460017480, 1190852520892329350092354441, 1270598627613805616203391468226138, 5381238039128882594932248239301142751179, 90766634183072089515270648224715368261615375340
Offset: 0
-
G(p)={my(n=serprec(p,x)); serconvol(p, sum(k=0, n-1, x^k/2^(k*(k-1)/2), O(x^n)))}
U(p)={my(n=serprec(p,x)); serconvol(p, sum(k=0, n-1, x^k*2^(k*(k-1)/2), O(x^n)))}
DigraphEgf(n)={sum(k=0, n, 2^(k*(k-1))*x^k/k!, O(x*x^n) )}
seq(n)={Vec(serlaplace(U(1/G(exp(x+log(U(1/G(DigraphEgf(n)))))))))} \\ Andrew Howroyd, Jan 15 2022
a(0)=1 prepended and terms a(12) and beyond from
Andrew Howroyd, Jan 15 2022
A361590
Triangle read by rows: T(n,k) is the number of digraphs on n unlabeled nodes with exactly k strongly connected components of size 1.
Original entry on oeis.org
1, 0, 1, 1, 0, 2, 5, 5, 0, 6, 90, 55, 42, 0, 31, 5289, 2451, 974, 592, 0, 302, 1071691, 323709, 94332, 29612, 15616, 0, 5984, 712342075, 135208025, 25734232, 6059018, 1650492, 795930, 0, 243668, 1585944117738, 181427072519, 21650983294, 3358042412, 704602272, 174576110, 79512478, 0, 20286025
Offset: 0
Triangle begins:
1;
0, 1;
1, 0, 2;
5, 5, 0, 6;
90, 55, 42, 0, 31;
5289, 2451, 974, 592, 0, 302;
1071691, 323709, 94332, 29612, 15616, 0, 5984;
...
A362013
Triangular array read by rows. T(n,k) is the number of labeled directed graphs on [n] with exactly k strongly connected components of size 1 with outdegree zero, n>=0, 0<=k<=n.
Original entry on oeis.org
1, 0, 1, 1, 2, 1, 27, 27, 9, 1, 2401, 1372, 294, 28, 1, 759375, 253125, 33750, 2250, 75, 1, 887503681, 171774906, 13852815, 595820, 14415, 186, 1, 3938980639167, 437664515463, 20841167403, 551353635, 8751645, 83349, 441, 1, 67675234241018881, 4263006881324024, 117484441611292, 1850148686792, 18210124870, 114709448, 451612, 1016, 1
Offset: 0
Triangle T(n,k) begins:
1;
0, 1;
1, 2, 1;
27, 27, 9, 1;
2401, 1372, 294, 28, 1;
759375, 253125, 33750, 2250, 75, 1;
...
-
nn = 6; B[n_] := n! 2^Binomial[n, 2] ; 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, 0, nn}]; Table[ Take[(Table[B[n], {n, 0, nn}] CoefficientList[ Series[ggf[Exp[(u - 1) z]]/ggf[Exp[-s[z]]], {z, 0, nn}], {z, u}])[[i]], i], {i, 1, nn + 1}]
Showing 1-3 of 3 results.
Comments