A036773 Number of labeled rooted trees with a degree constraint: ((5*n)!/(120^n)) * C(5*n+1, n).

1, 6, 13860, 423783360, 70220478968640, 41004669682770393600, 65405789473547026656472320, 240729724316568938710767014707200, 1813083536072533851678174232377806438400, 25541737277107694920826740625991927645705830400

Offset

0,2

Links

Table of n, a(n) for n=0..9.

Lajos Takács, Enumeration of rooted trees and forests, Math. Scientist 18 (1993), 1-10; see Eq. (13) on p. 4 (with r = 5). [Wayback Machine link]

Index entries for sequences related to rooted trees.

Formula

E.g.f. with interpolated zeros: Let G(x) = Sum_{n >= 0} a(n)*x^(5*n + 1)/(5*n + 1)!. Then this e.g.f. satisfies the equation G(x) = x*(1 + G(x)^5/5!). - Petros Hadjicostas, Jun 08 2019

a(n) ~ 5^(9*n+2) * (n/e)^(5*n) / (2^(11*n+3) * 3^n). - Amiram Eldar, Oct 12 2025

Mathematica

a[n_] := (5*n)! * Binomial[5*n+1, n] / 120^n; Array[a, 10, 0] (* Amiram Eldar, Oct 12 2025 *)

Crossrefs

Cf. A036770, A036771, A036772.

Sequence in context: A145720 A093897 A062782 * A007702 A112642 A130434

Adjacent sequences: A036770 A036771 A036772 * A036774 A036775 A036776

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved