OFFSET
0,2
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..855
Alexander Burstein and Louis W. Shapiro, Pseudo-involutions in the Riordan group, arXiv:2112.11595 [math.CO], 2021-2022.
Clemens Heuberger, Sarah J. Selkirk, and Stephan Wagner, Enumeration of Generalized Dyck Paths Based on the Height of Down-Steps Modulo k, arXiv:2204.14023 [math.CO], 2022.
FORMULA
a(n) = 3*binomial(6*n+3,n)/(6*n+3).
G.f.: A(x) = G(x)^3 where G(x) = 1 + x*G(x)^6 is the g.f. of A002295.
a(n) ~ 3^(6*n+7/2) * 4^(3*n+1) / (5^(5*n+7/2) * n^(3/2) * sqrt(Pi)). - Amiram Eldar, Sep 13 2025
EXAMPLE
MATHEMATICA
Table[(3 Binomial[#, n])/# &[6 n + 3], {n, 0, 20}] (* Michael De Vlieger, May 13 2022 *)
PROG
(PARI) {a(n)=binomial(6*n+3, n) * 3/(6*n+3)}
for(n=0, 40, print1(a(n), ", "))
(PARI) {a(n)=local(A=1+3*x); for(i=1, n, A=(1+x*A^2)^3+x*O(x^n)); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 29 2012
STATUS
approved