A060337 Number of labeled acyclic digraphs with n nodes containing exactly n-2 points of in-degree zero.

15, 198, 1610, 10575, 61845, 336924, 1751076, 8801325, 43141175, 207347778, 980828238, 4578689115, 21135851625, 96628899960, 438068838536, 1971349880985, 8813183238315, 39169902510270, 173172640973010

Offset: 3

Author

Vladeta Jovovic, Apr 10 2001

Keywords

• nonn
• easy

References

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 3..500
• Index entries for linear recurrences with constant coefficients, signature (21,-189,955,-2982,5964,-7640,6048,-2688,512).

Crossrefs

Third column of A058876.

Cf. A003025, A003026.

Programs

Mathematica

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 *)

PARI

\\ requires A058876.
my(T=A058876(25)); vector(#T-2, n, T[n+2][n]) \\ Andrew Howroyd, Dec 27 2021

Formula

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