A100569 - OEIS

%I #13 Feb 23 2019 07:03:06

%S 1,1,1,9,337,37889,11410545,9368733289,21760617258977,

%T 146872848650637249,2927557787922534645793,

%U 173801937725990883065857673,30857177979379449393077427767217,16413568090264759380752395628891885377,26177914283033566658965502231213434987939601

%N Number of labeled n-node oriented graphs without endpoints.

%H Andrew Howroyd, <a href="/A100569/b100569.txt">Table of n, a(n) for n = 0..50</a>

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

%t m = 14;

%t egf = Exp[x^2]*Sum[3^(n (n - 1)/2)*(x/Exp[2 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(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

%Y Cf. A059167.

%K nonn

%O 0,4

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

%E Terms a(13) and beyond from _Andrew Howroyd_, Sep 09 2018