OFFSET
0,2
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = (8*(2*n - 1) * (4*n - 3) * (4*n - 1) * a(n - 1)) / (3*n * (3*n - 2) * (3*n - 1))) for n >= 2.
a(n) = [x^n] C(x)^(2*n), where C(x) = (1 - sqrt(1 - 4*x))/(2*x) is the g.f. of the Catalan numbers A000108. - Peter Bala, Apr 27 2023
MAPLE
a := n -> ifelse(n = 0, 1, 2*binomial(4*n - 1, 3*n)):
# Alternative:
a := proc(n) option remember; ifelse(n < 2, n + 1, (8*(2*n - 1) * (4*n - 3) * (4*n - 1) * a(n - 1)) / (3 * n * (3*n - 2) * (3*n - 1))) end:
seq(a(n), n = 0..19);
MATHEMATICA
A359108[n_] := If[n == 0, 1, 2*Binomial[4*n - 1, 3*n]];
Array[A359108, 25, 0] (* Paolo Xausa, Sep 18 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Dec 27 2022
STATUS
approved