A036772 Number of labeled rooted trees with a degree constraint: ((4*n)!/(24^n)) * binomial(4*n+1, n).

1, 5, 2520, 9909900, 150089940000, 6217438242015000, 574985352122181000000, 103753754577643425255000000, 33189544956070738228953960000000, 17517292900368819935211385551000000000, 14427024664929016470240101675459976000000000

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 = 4).
• Index entries for sequences related to rooted trees

Crossrefs

Cf. A036770, A036771, A036773.

Programs

Mathematica

Table[(4n)!/24^n Binomial[4n+1,n],{n,0,10}] (* Harvey P. Dale, Aug 10 2011 *)

Formula

From Petros Hadjicostas, Jun 08 2019: (Start)

Recurrence (with no interpolated zeros): -8 * (4*n + 1) * (4*n + 3)^2 * (2*n + 1)^2 * (4*n + 5) * a(n) + (81*n^2 + 162*n + 72) * a(n + 1) = 0 for n >= 0 with a(0) = 1.

E.g.f. (with interpolated zeros): Let G(x) = Sum_{n >= 0} a(n)*x^(4*n + 1)/(4*n + 1)!. Then the e.g.f. satisfies G(x) = x * (1 + G(x)^4/4!).

(End)