A100569 Number of labeled n-node oriented graphs without endpoints.

1, 1, 1, 9, 337, 37889, 11410545, 9368733289, 21760617258977, 146872848650637249, 2927557787922534645793, 173801937725990883065857673, 30857177979379449393077427767217, 16413568090264759380752395628891885377, 26177914283033566658965502231213434987939601

Offset

0,4

Links

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

Formula

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

Mathematica

m = 14;
egf = Exp[x^2]*Sum[3^(n (n - 1)/2)*(x/Exp[2 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 *)

Prog

(PARI) seq(n)={my(A=x/exp(2*x+O(x^n))); Vec(serlaplace(exp(x^2 + O(x*x^n)) * sum(k=0, n, 3^binomial(k, 2)*A^k/k!)))} \\ Andrew Howroyd, Sep 09 2018

Crossrefs

Cf. A059167.

Sequence in context: A303208 A196883 A012105 * A244503 A152553 A090087

Adjacent sequences: A100566 A100567 A100568 * A100570 A100571 A100572

Keyword

nonn

Author

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

Extensions

Terms a(13) and beyond from Andrew Howroyd, Sep 09 2018

Status

approved