A366216 -id:A366216 - cp's OEIS frontend

A366200 G.f. A(x) satisfies A(x) = 1 + x(1 + x)^3A(x)^3.

1, 1, 6, 33, 209, 1425, 10206, 75751, 577494, 4495368, 35582439, 285524184, 2317387098, 18990744137, 156918815760, 1305927563487, 10936673012579, 92098612059051, 779391530714589, 6624730079900931, 56532669993156696, 484156547579505717, 4159926573597719575

Offset: 0

Seiichi Manyama, Oct 04 2023

nonn

Cf. A073155, A366216.

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

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

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

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Dec 07 2024

nonn

Cf. A365178, A366216, A366272.
Cf. A002478, A073155, A366221.
Cf. A002293.

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));

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).

cp's OEIS Frontend

A366200 G.f. A(x) satisfies A(x) = 1 + x(1 + x)^3A(x)^3.

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

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cp's OEIS Frontend

A366200 G.f. A(x) satisfies A(x) = 1 + x*(1 + x)^3*A(x)^3.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

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

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Author

Keywords

Crossrefs

Programs

PARI

Formula

A366200 G.f. A(x) satisfies A(x) = 1 + x(1 + x)^3A(x)^3.