A371576 G.f. satisfies A(x) = ( 1 + x*A(x)^(3/2) * (1 + x) )^2.

1, 2, 9, 44, 240, 1390, 8404, 52426, 334964, 2180928, 14418123, 96525656, 653077411, 4458529390, 30674865164, 212472058410, 1480446579602, 10369560147798, 72972217926122, 515674254743332, 3657933383804959, 26036659997517572, 185905008055923918

Offset: 0

Author

Seiichi Manyama, Mar 28 2024

Keywords

• nonn

Crossrefs

Column k=2 of A378323.

Cf. A001629, A052705, A371577, A371578.

Cf. A270386, A364475.

Programs

PARI

a(n, r=2, s=1, t=3, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));

Formula

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

G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A364475.