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

3,1

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).

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

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 *)

Prog

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

Crossrefs

Third column of A058876.

Cf. A003025, A003026.

Sequence in context: A185899 A345445 A152587 * A180789 A078264 A322914

Adjacent sequences: A060334 A060335 A060336 * A060338 A060339 A060340

Keyword

nonn,easy

Author

Vladeta Jovovic, Apr 10 2001

Status

approved