A378786 G.f. A(x) satisfies A(x) = 1 + x * (1+x)^2 * A(x)^4.

1, 1, 6, 39, 296, 2435, 21138, 190603, 1767968, 16761424, 161697576, 1582171216, 15664531716, 156637712953, 1579664567130, 16048129755157, 164085811289360, 1687224436103842, 17436287104620980, 181001686332329224, 1886522317836670988, 19734386503541838083

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=0..n} binomial(4*k+1,k) * binomial(2*k,n-k)/(4*k+1) = Sum_{k=0..n} binomial(2*k,n-k) * A002293(k).

Prog

(PARI) a(n, r=1, s=2, t=4, 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));

Crossrefs

Cf. A365178, A366216, A366272.

Cf. A002478, A073155, A366221.

Cf. A002293.

Sequence in context: A103194 A009018 A289996 * A335344 A135890 A067273

Adjacent sequences: A378783 A378784 A378785 * A378787 A378788 A378789

Keyword

nonn

Author

Seiichi Manyama, Dec 07 2024

Status

approved