OFFSET
0,2
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..1025
N. J. Wildberger and Dean Rubine, A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode, Amer. Math. Monthly, Vol. 132, No. 5 (2025), pp. 383-402. See section 12.
FORMULA
The o.g.f. equals f(x)*g(x)^2, where f(x) is the o.g.f. for A005810 and g(x) is the o.g.f. for A002293. More generally, f(x)*g(x)^k is the o.g.f. for the sequence binomial(4*n + k,n). Cf. A262977 (k = -1), A005810 (k = 0), A052203 (k = 1), A224274 (k = 3) and A004331 (k = 4).
a(n) ~ 2^(8*n+9/2) / (3^(3*n+5/2) * sqrt(Pi*n)). - Amiram Eldar, Sep 21 2025
MAPLE
seq(binomial(4*n + 2, n), n = 0..20);
MATHEMATICA
Table[Binomial[4*n + 2, n], {n, 0, 120}] (* Michael De Vlieger, Apr 11 2025 *)
PROG
(PARI) vector(30, n, n--; binomial(4*n+2, n)) \\ Altug Alkan, Nov 05 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Bala, Nov 04 2015
STATUS
approved