A257633 a(n) = binomial(4*n + 2,n).

1, 6, 45, 364, 3060, 26334, 230230, 2035800, 18156204, 163011640, 1471442973, 13340783196, 121399651100, 1108176102180, 10142940735900, 93052749919920, 855420636763836, 7877932561061640, 72667580816130436, 671262558647881200, 6208770443303347920

Offset: 0

Author

Peter Bala, Nov 04 2015

Keywords

• nonn
• easy

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 (2025). See section 12.

Crossrefs

Cf. A002293, A004331, A005810, A052203, A224274, A262977.

Programs

Maple

#A257633
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 *)

PARI

vector(30, n, n--; binomial(4*n+2, n)) \\ Altug Alkan, Nov 05 2015

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).