login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Number of labeled acyclic digraphs with n nodes containing exactly n-2 points of in-degree zero.
2

%I #10 Mar 23 2022 14:45:32

%S 15,198,1610,10575,61845,336924,1751076,8801325,43141175,207347778,

%T 980828238,4578689115,21135851625,96628899960,438068838536,

%U 1971349880985,8813183238315,39169902510270,173172640973010

%N Number of labeled acyclic digraphs with n nodes containing exactly n-2 points of in-degree zero.

%D F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 19, (1.6.4).

%D R. W. Robinson, Counting labeled acyclic digraphs, pp. 239-273 of F. Harary, editor, New Directions in the Theory of Graphs. Academic Press, NY, 1973.

%H Andrew Howroyd, <a href="/A060337/b060337.txt">Table of n, a(n) for n = 3..500</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (21,-189,955,-2982,5964,-7640,6048,-2688,512).

%F G.f.: x^3*(15 - 117*x + 287*x^2 - 138*x^3 - 300*x^4 + 280*x^5)/((1 - x)*(1 - 2*x)*(1 - 4*x))^3. - _Andrew Howroyd_, Dec 27 2021

%t LinearRecurrence[{21,-189,955,-2982,5964,-7640,6048,-2688,512},{15,198,1610,10575,61845,336924,1751076,8801325,43141175},20] (* _Harvey P. Dale_, Mar 23 2022 *)

%o (PARI) \\ requires A058876.

%o my(T=A058876(25)); vector(#T-2, n, T[n+2][n]) \\ _Andrew Howroyd_, Dec 27 2021

%Y Third column of A058876.

%Y Cf. A003025, A003026.

%K nonn,easy

%O 3,1

%A _Vladeta Jovovic_, Apr 10 2001