|
|
A100548
|
|
Number of n-node labeled digraphs without endpoints.
|
|
3
|
|
|
1, 1, 1, 28, 2539, 847126, 987474781, 4267529230672, 71328353711113801, 4706871807383903992060, 1236666872833000506726110479, 1297665884376581511952494336126664, 5444003907104081585974782986977125743035, 91341304409373044577470623665964376840167100920
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: exp(3/2*x^2)*(Sum_{n>=0} 2^(n*(n-1))*(x/exp(3*x))^n/n!).
|
|
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!;
|
|
PROG
|
(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
(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<x>:=PowerSeriesRing(Rationals(), m);
(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) )
P.<x> = PowerSeriesRing(QQ, prec)
return P( f(x) ).egf_to_ogf().list()
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|