A366267 G.f. A(x) satisfies A(x) = 1 + x + x*A(x)^4.

1, 2, 8, 56, 448, 3920, 36288, 349440, 3464448, 35125760, 362522624, 3795914240, 40224968704, 430579701760, 4648899846144, 50568103690240, 553632271155200, 6096025799852032, 67464070696927232, 750003531943903232, 8371814935842258944

Offset

0,2

Links

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

Formula

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

a(n) = A366272(n) + A366272(n-1).

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366365.

Mathematica

nmax = 20; A[_] = 1;
Do[A[x_] = 1 + x + x*A[x]^4 + O[x]^(nmax+1) // Normal, {nmax+1}];
CoefficientList[A[x], x] (* Jean-François Alcover, Mar 03 2024 *)

Prog

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

Crossrefs

Cf. A025227, A366266, A366268.

Cf. A366272, A366365.

Sequence in context: A333564 A291314 A354248 * A308501 A316142 A109618

Adjacent sequences: A366264 A366265 A366266 * A366268 A366269 A366270

Keyword

nonn

Author

Seiichi Manyama, Oct 06 2023

Status

approved