OFFSET
0,2
LINKS
L. Takacs, Enumeration of rooted trees and forests, Math. Scientist 18 (1993), 1-10; see Eq. (13) on p. 4 (with r = 4).
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)
MATHEMATICA
Table[(4n)!/24^n Binomial[4n+1, n], {n, 0, 10}] (* Harvey P. Dale, Aug 10 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved