A371891 G.f. A(x) satisfies A(x) = 1 - x/A(x)^2 * (1 - A(x) - A(x)^4).

1, 1, 3, 8, 21, 61, 203, 724, 2600, 9291, 33525, 123537, 463796, 1759184, 6706976, 25696524, 99069838, 384429159, 1499778661, 5875513183, 23099489574, 91123553946, 360649997698, 1431724692900, 5699142280127, 22741352276386, 90949212893978

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

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

Prog

(PARI) a(n) = if(n==0, 1, sum(k=0, n, binomial(n, k)*binomial(2*n-4*k, n-k-1))/n);

Crossrefs

Cf. A349331, A364748, A367724, A371890.

Sequence in context: A018037 A018038 A000737 * A192235 A148769 A361574

Adjacent sequences: A371888 A371889 A371890 * A371892 A371893 A371894

Keyword

nonn

Author

Seiichi Manyama, Apr 11 2024

Status

approved