A378787 G.f. A(x) satisfies A(x) = ( 1 + x * (1 + x*A(x)^2)^3 )^2.

1, 2, 7, 36, 197, 1184, 7425, 48308, 322521, 2198064, 15227850, 106924154, 759245463, 5442675080, 39335090088, 286296369000, 2096706604597, 15439417451928, 114243931954962, 849030345258990, 6334510149389409, 47428709540589036, 356261301882333885

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

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

G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A137957.

Prog

(PARI) a(n, r=2, s=3, t=0, u=4) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A069271, A371607, A371609.

Cf. A137957.

Sequence in context: A192816 A302895 A302905 * A249691 A129261 A371545

Adjacent sequences: A378781 A378782 A378786 * A378788 A378790 A378791

Keyword

nonn,new

Author

Seiichi Manyama, Dec 07 2024

Status

approved