A371609 G.f. satisfies A(x) = ( 1 + x * (1 + x*A(x)^2)^2 )^2.

1, 2, 5, 22, 94, 452, 2253, 11640, 61732, 333924, 1836052, 10229434, 57628078, 327711260, 1878658490, 10845298128, 62993496588, 367874945560, 2158717741928, 12722258713956, 75269561054412, 446891212180568, 2661788871400197, 15900644226590952, 95240143776976144

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

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

G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A137955.

Prog

(PARI) a(n, r=2, s=2, 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. A137955, A371614.

Sequence in context: A307155 A144934 A346628 * A030222 A362790 A369830

Adjacent sequences: A371606 A371607 A371608 * A371610 A371611 A371612

Keyword

nonn

Author

Seiichi Manyama, Mar 29 2024

Status

approved