cp's OEIS Frontend

A100548 Number of n-node labeled digraphs without endpoints.

%I A100548 #17 Mar 28 2023 08:00:11
%S A100548 1,1,1,28,2539,847126,987474781,4267529230672,71328353711113801,
%T A100548 4706871807383903992060,1236666872833000506726110479,
%U A100548 1297665884376581511952494336126664,5444003907104081585974782986977125743035,91341304409373044577470623665964376840167100920
%N A100548 Number of n-node labeled digraphs without endpoints.
%H A100548 Andrew Howroyd, <a href="/A100548/b100548.txt">Table of n, a(n) for n = 0..50</a>
%F A100548 E.g.f.: exp(3/2*x^2)*(Sum_{n>=0} 2^(n*(n-1))*(x/exp(3*x))^n/n!).
%t A100548 m = 11;
%t A100548 egf = Exp[3x^2/2]*Sum[2^(n(n-1))*(x/Exp[3 x])^n/n!, {n, 0, m}];
%t A100548 a[n_] := SeriesCoefficient[egf, {x, 0, n}]*n!;
%t A100548 Table[a[n], {n, 0, m}] (* _Jean-François Alcover_, Feb 23 2019 *)
%o A100548 (PARI) seq(n)={my(g=x/exp(3*x + O(x*x^n))); Vec(serlaplace(exp(3*x^2/2 + O(x*x^n))*sum(k=0, n, 2^(k*(k-1))*g^k/k!)))} \\ _Andrew Howroyd_, Jan 08 2020
%o A100548 (Magma)
%o A100548 m:=30;
%o A100548 f:= func< x | Exp(3*x^2/2)*(&+[ 2^(n*(n-1))*(x*Exp(-3*x))^n/Factorial(n) : n in [0..m+2]]) >;
%o A100548 R<x>:=PowerSeriesRing(Rationals(), m);
%o A100548 Coefficients(R!(Laplace( f(x) ))); // _G. C. Greubel_, Mar 27 2023
%o A100548 (SageMath)
%o A100548 m = 30
%o A100548 def f(x): return exp(3*x^2/2)*sum( 2^(n*(n-1))*(x*exp(-3*x))^n/factorial(n) for n in range(m+2) )
%o A100548 def A100548_list(prec):
%o A100548     P.<x> = PowerSeriesRing(QQ, prec)
%o A100548     return P( f(x) ).egf_to_ogf().list()
%o A100548 A100548_list(m) # _G. C. Greubel_, Mar 27 2023
%Y A100548 Cf. A059167, A101388 (labeled case).
%K A100548 nonn
%O A100548 0,4
%A A100548 Goran Kilibarda, Zoran Maksimovic, _Vladeta Jovovic_, Jan 02 2005
%E A100548 Terms a(12) and beyond from _Andrew Howroyd_, Jan 08 2020