|
| |
|
|
A054941
|
|
Number of weakly connected oriented graphs on n labeled nodes.
|
|
10
|
|
|
|
1, 2, 20, 624, 55248, 13982208, 10358360640, 22792648882176, 149888345786341632, 2952810709943411146752, 174416705255313941476193280, 30901060796613886817249881227264, 16422801513633911416125344647746244608, 26183660776604240464418800095675915958222848
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
The triangle of oriented labeled graphs on n>=1 nodes with 1<=k<=n components and row sums A047656 starts:
1;
2, 1;
20, 6, 1;
624, 92, 12, 1;
55248, 3520, 260, 20, 1;
13982208, 354208, 11880, 580, 30, 1; - R. J. Mathar, Apr 29 2019
|
|
|
LINKS
|
Seiichi Manyama, Table of n, a(n) for n = 1..65
V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.
|
|
|
FORMULA
|
E.g.f.: log( Sum_{n >= 0} 3^binomial(n, 2)*x^n/n! ). - Vladeta Jovovic, Feb 14 2003
|
|
|
MATHEMATICA
|
nn=20; s=Sum[3^Binomial[n, 2]x^n/n!, {n, 0, nn}]; Drop[Range[0, nn]! CoefficientList[Series[Log[s]+1, {x, 0, nn}], x], 1] (* Geoffrey Critzer, Oct 22 2012 *)
|
|
|
PROG
|
(PARI) N=20; x='x+O('x^N); Vec(serlaplace(log(sum(k=0, N, 3^binomial(k, 2)*x^k/k!)))) \\ Seiichi Manyama, May 18 2019
|
|
|
CROSSREFS
|
Row sums of A350732.
The unlabeled version is A086345.
Cf. A001187 (graphs), A003027 (digraphs), A350730 (strongly connected).
Sequence in context: A197743 A009182 A015207 * A012495 A168480 A198761
Adjacent sequences: A054938 A054939 A054940 * A054942 A054943 A054944
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane, May 24 2000
|
|
|
EXTENSIONS
|
More terms from Vladeta Jovovic, Feb 14 2003
|
|
|
STATUS
|
approved
|
| |
|
|
