A372086 G.f. A(x) satisfies A(x) = 1/( 1 - 4*x*(1 + x)*A(x) )^(1/2).

1, 2, 12, 84, 664, 5624, 49928, 458480, 4318896, 41503168, 405267840, 4009684608, 40109536992, 404977089792, 4121810315584, 42243756499328, 435593319238144, 4515817056202496, 47040399766319360, 492117122988795392, 5168258741713256960

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} 4^k * binomial(3*k/2-1/2,k) * binomial(k,n-k)/(k+1).

Prog

(PARI) a(n) = sum(k=0, n, 4^k*binomial(3*k/2-1/2, k)*binomial(k, n-k)/(k+1));

Crossrefs

Cf. A006139, A372037.

Sequence in context: A105927 A316702 A235351 * A362245 A362237 A052887

Adjacent sequences: A372062 A372084 A372085 * A372087 A372088 A372089

Keyword

nonn

Author

Seiichi Manyama, Apr 17 2024

Status

approved