%I #17 Mar 28 2023 08:00:11

%S 1,1,1,28,2539,847126,987474781,4267529230672,71328353711113801,

%T 4706871807383903992060,1236666872833000506726110479,

%U 1297665884376581511952494336126664,5444003907104081585974782986977125743035,91341304409373044577470623665964376840167100920

%N Number of n-node labeled digraphs without endpoints.

%H Andrew Howroyd, <a href="/A100548/b100548.txt">Table of n, a(n) for n = 0..50</a>

%F E.g.f.: exp(3/2*x^2)*(Sum_{n>=0} 2^(n*(n-1))*(x/exp(3*x))^n/n!).

%t m = 11;

%t egf = Exp[3x^2/2]*Sum[2^(n(n-1))*(x/Exp[3 x])^n/n!, {n, 0, m}];

%t a[n_] := SeriesCoefficient[egf, {x, 0, n}]*n!;

%t Table[a[n], {n, 0, m}] (* _Jean-François Alcover_, Feb 23 2019 *)

%o (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 (Magma)

%o m:=30;

%o 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 R<x>:=PowerSeriesRing(Rationals(), m);

%o Coefficients(R!(Laplace( f(x) ))); // _G. C. Greubel_, Mar 27 2023

%o (SageMath)

%o m = 30

%o 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 def A100548_list(prec):

%o P.<x> = PowerSeriesRing(QQ, prec)

%o return P( f(x) ).egf_to_ogf().list()

%o A100548_list(m) # _G. C. Greubel_, Mar 27 2023

%Y Cf. A059167, A101388 (labeled case).

%K nonn

%O 0,4

%A Goran Kilibarda, Zoran Maksimovic, _Vladeta Jovovic_, Jan 02 2005

%E Terms a(12) and beyond from _Andrew Howroyd_, Jan 08 2020