A100548 Number of n-node labeled digraphs without endpoints.

1, 1, 1, 28, 2539, 847126, 987474781, 4267529230672, 71328353711113801, 4706871807383903992060, 1236666872833000506726110479, 1297665884376581511952494336126664, 5444003907104081585974782986977125743035, 91341304409373044577470623665964376840167100920

Offset: 0

Author

Goran Kilibarda, Zoran Maksimovic, Vladeta Jovovic, Jan 02 2005

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A059167, A101388 (labeled case).

Programs

Magma

m:=30;
f:= func< x | Exp(3*x^2/2)*(&+[ 2^(n*(n-1))*(x*Exp(-3*x))^n/Factorial(n) : n in [0..m+2]]) >;
R:=PowerSeriesRing(Rationals(), m);
Coefficients(R!(Laplace( f(x) ))); // G. C. Greubel, Mar 27 2023

Mathematica

m = 11;
egf = Exp[3x^2/2]*Sum[2^(n(n-1))*(x/Exp[3 x])^n/n!, {n, 0, m}];
a[n_] := SeriesCoefficient[egf, {x, 0, n}]*n!;
Table[a[n], {n, 0, m}] (* Jean-François Alcover, Feb 23 2019 *)

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

SageMath

m = 30
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) )
def A100548_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( f(x) ).egf_to_ogf().list()
A100548_list(m) # G. C. Greubel, Mar 27 2023

Formula

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

Extensions

Terms a(12) and beyond from Andrew Howroyd, Jan 08 2020