A379254 G.f. A(x) satisfies A(x) = ( (1 + x*A(x))/(1 - x*A(x)^2) )^3.

1, 6, 72, 1136, 20496, 400176, 8230592, 175643712, 3852905472, 86338960640, 1967950718976, 45483461999616, 1063433350498304, 25107661327202304, 597766180153565184, 14335020154675867648, 345948883288769740800, 8395511682729703931904

Offset: 0

Author

Seiichi Manyama, Dec 19 2024

Keywords

• nonn

Crossrefs

Cf. A213282, A365843, A379255.

Cf. A379256.

Programs

PARI

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

Formula

G.f.: B(x)^3 where B(x) is the g.f. of A379256.

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