cp's OEIS Frontend

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

%I A054941 #31 Apr 29 2023 08:10:29
%S A054941 1,2,20,624,55248,13982208,10358360640,22792648882176,
%T A054941 149888345786341632,2952810709943411146752,
%U A054941 174416705255313941476193280,30901060796613886817249881227264,16422801513633911416125344647746244608,26183660776604240464418800095675915958222848
%N A054941 Number of weakly connected oriented graphs on n labeled nodes.
%C A054941 The triangle of oriented labeled graphs on n>=1 nodes with 1<=k<=n components and row sums A047656 starts:
%C A054941        1;
%C A054941        2,      1;
%C A054941       20,      6,     1;
%C A054941      624,     92,    12,   1;
%C A054941    55248,   3520,   260,  20,  1;
%C A054941 13982208, 354208, 11880, 580, 30, 1; - _R. J. Mathar_, Apr 29 2019
%H A054941 Seiichi Manyama, <a href="/A054941/b054941.txt">Table of n, a(n) for n = 1..65</a>
%H A054941 V. A. Liskovets, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/LISK/Derseq.html">Some easily derivable sequences</a>, J. Integer Sequences, 3 (2000), #00.2.2.
%F A054941 E.g.f.: log( Sum_{n >= 0} 3^binomial(n, 2)*x^n/n! ). - _Vladeta Jovovic_, Feb 14 2003
%t A054941 nn=20; s=Sum[3^Binomial[n,2]x^n/n!,{n,0,nn}];
%t A054941 Drop[Range[0,nn]! CoefficientList[Series[Log[s]+1,{x,0,nn}],x],1] (* _Geoffrey Critzer_, Oct 22 2012 *)
%o A054941 (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
%o A054941 (Magma)
%o A054941 m:=30;
%o A054941 f:= func< x | (&+[3^Binomial(n,2)*x^n/Factorial(n) : n in [0..m+3]]) >;
%o A054941 R<x>:=PowerSeriesRing(Rationals(), m);
%o A054941 Coefficients(R!(Laplace( Log(f(x)) ))); // _G. C. Greubel_, Apr 28 2023
%o A054941 (SageMath)
%o A054941 m=30
%o A054941 def f(x): return sum(3^binomial(n,2)*x^n/factorial(n) for n in range(m+4))
%o A054941 def A054941_list(prec):
%o A054941     P.<x> = PowerSeriesRing(QQ, prec)
%o A054941     return P( log(f(x)) ).egf_to_ogf().list()
%o A054941 a=A054941_list(40); a[1:] # _G. C. Greubel_, Apr 28 2023
%Y A054941 Row sums of A350732.
%Y A054941 The unlabeled version is A086345.
%Y A054941 Cf. A001187 (graphs), A003027 (digraphs), A350730 (strongly connected).
%K A054941 nonn,easy
%O A054941 1,2
%A A054941 _N. J. A. Sloane_, May 24 2000
%E A054941 More terms from _Vladeta Jovovic_, Feb 14 2003