A366272 G.f. A(x) satisfies A(x) = 1 + x*(1 + x)^3*A(x)^4.

1, 1, 7, 49, 399, 3521, 32767, 316673, 3147775, 31977985, 330544639, 3465369601, 36759599103, 393820102657, 4255079743487, 46313023946753, 507319247208447, 5588706552643585, 61875364144283647, 688128167799619585, 7683686768042639359

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=0..n} binomial(3*k,n-k) * binomial(4*k,k)/(3*k+1).

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366436.

Prog

(PARI) a(n) = sum(k=0, n, binomial(3*k, n-k)*binomial(4*k, k)/(3*k+1));

Crossrefs

Cf. A052709, A366221, A366273.

Cf. A366267, A366436.

Sequence in context: A343583 A221462 A374855 * A366501 A090016 A005924

Adjacent sequences: A366269 A366270 A366271 * A366273 A366274 A366275

Keyword

nonn

Author

Seiichi Manyama, Oct 06 2023

Status

approved