A379283 G.f. A(x) satisfies A(x) = 1/( (1 - x*A(x)^3) * (1 - x*A(x)) )^2.

1, 4, 42, 612, 10387, 192312, 3766316, 76716624, 1608691229, 34495221722, 752911467734, 16671973428486, 373609441084507, 8457057155407906, 193087102810266948, 4441320670474030222, 102821800799622552713, 2394063264658388861914, 56025225620739219372819

Offset: 0

Author

Seiichi Manyama, Dec 19 2024

Keywords

• nonn

Crossrefs

Cf. A379244, A379252, A379280.

Cf. A379281, A379282.

Cf. A379189, A379287.

Programs

PARI

a(n) = 2*sum(k=0, n, binomial(2*n+5*k+2, k)*binomial(3*n+3*k+1, n-k)/(2*n+5*k+2));

Formula

G.f.: B(x)^2 where B(x) is the g.f. of A379287.

a(n) = 2 * Sum_{k=0..n} binomial(2*n+5*k+2,k) * binomial(3*n+3*k+1,n-k)/(2*n+5*k+2).