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

Author

N. J. A. Sloane

Keywords

• nonn

Links

• L. Takacs, Enumeration of rooted trees and forests, Math. Scientist 18 (1993), 1-10; see Eq. (13) on p. 4 (with r = 5).
• Index entries for sequences related to rooted trees

Crossrefs

Cf. A036770, A036771, A036772.

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