A054941 Number of weakly connected oriented graphs on n labeled nodes.

1, 2, 20, 624, 55248, 13982208, 10358360640, 22792648882176, 149888345786341632, 2952810709943411146752, 174416705255313941476193280, 30901060796613886817249881227264, 16422801513633911416125344647746244608, 26183660776604240464418800095675915958222848

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
(Magma)
m:=30;
f:= func< x | (&+[3^Binomial(n, 2)*x^n/Factorial(n) : n in [0..m+3]]) >;
R<x>:=PowerSeriesRing(Rationals(), m);
Coefficients(R!(Laplace( Log(f(x)) ))); // G. C. Greubel, Apr 28 2023
(SageMath)
m=30
def f(x): return sum(3^binomial(n, 2)*x^n/factorial(n) for n in range(m+4))
def A054941_list(prec):
    P.<x> = PowerSeriesRing(QQ, prec)
    return P( log(f(x)) ).egf_to_ogf().list()
a=A054941_list(40); a[1:] # G. C. Greubel, Apr 28 2023

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 A364886

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