A361588
Triangle read by rows: T(n,k) is the number of digraphs on n unlabeled nodes with k strongly connected components and without isolated nodes.
Original entry on oeis.org
1, 0, 0, 0, 1, 1, 0, 5, 4, 4, 0, 83, 57, 37, 25, 0, 5048, 2411, 1110, 550, 271, 0, 1047008, 325015, 101467, 37140, 15024, 5682, 0, 705422362, 136887749, 27765860, 7139149, 2259378, 780314, 237684, 0, 1580348371788, 183852357683, 23088181536, 3923330808, 907186816, 258971872, 78716548, 20042357
Offset: 0
Triangle begins:
1;
0, 0;
0, 1, 1;
0, 5, 4, 4;
0, 83, 57, 37, 25;
0, 5048, 2411, 1110, 550, 271;
0, 1047008, 325015, 101467, 37140, 15024, 5682;
...
A361455
Triangle read by rows: T(n,k) is the number of simple digraphs on labeled n nodes with k strongly connected components.
Original entry on oeis.org
1, 0, 1, 0, 1, 3, 0, 18, 21, 25, 0, 1606, 1173, 774, 543, 0, 565080, 271790, 122595, 59830, 29281, 0, 734774776, 229224750, 70500705, 25349355, 10110735, 3781503, 0, 3523091615568, 685793359804, 138122171880, 35130437825, 11002159455, 3767987307, 1138779265
Offset: 0
Triangle begins:
1;
0, 1;
0, 1, 3;
0, 18, 21, 25;
0, 1606, 1173, 774, 543;
0, 565080, 271790, 122595, 59830, 29281;
0, 734774776, 229224750, 70500705, 25349355, 10110735, 3781503;
...
-
Z(p, f)={my(n=serprec(p, x)); serconvol(p, sum(k=0, n-1, x^k*f(k), O(x^n)))}
G(e, p)={Z(p, k->1/e^(k*(k-1)/2))}
U(e, p)={Z(p, k->e^(k*(k-1)/2))}
DigraphEgf(n, e)={sum(k=0, n, e^(k*(k-1))*x^k/k!, O(x*x^n) )}
T(n)={my(e=2); [Vecrev(p) | p<-Vec(serlaplace(U(e, 1/G(e, exp(y*log(U(e, 1/G(e, DigraphEgf(n, e)))))))))]}
{ my(A=T(6)); for(i=1, #A, print(A[i])) }
A361587
Triangle read by rows: T(n,k) is the number of weakly connected digraphs on n unlabeled nodes with k strongly connected components.
Original entry on oeis.org
1, 0, 1, 0, 1, 1, 0, 5, 4, 4, 0, 83, 56, 36, 24, 0, 5048, 2406, 1101, 542, 267, 0, 1047008, 324917, 101307, 37017, 14947, 5647, 0, 705422362, 136882286, 27757789, 7134897, 2257234, 779257, 237317, 0, 1580348371788, 183851281949, 23086772643, 3922864504, 907027520, 258909828, 78691767, 20035307
Offset: 0
Triangle begins:
1;
0, 1;
0, 1, 1;
0, 5, 4, 4;
0, 83, 56, 36, 24;
0, 5048, 2406, 1101, 542, 267;
0, 1047008, 324917, 101307, 37017, 14947, 5647;
...
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;
...
Showing 1-4 of 4 results.