A365181 G.f. satisfies A(x) = 1 + x*A(x)^4*(1 + x*A(x)^2).

1, 1, 5, 32, 237, 1905, 16160, 142392, 1290613, 11955947, 112697701, 1077438356, 10422562156, 101827196684, 1003312506776, 9958506719664, 99479743121349, 999370184665407, 10090067735619023, 102330789530653912, 1041997707624103589, 10648963961114066129

Offset

0,3

Links

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

Formula

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

Mathematica

terms = 22; A[_] = 0; Do[A[x_] = 1 + x*A[x]^4*(1 + x *A[x]^2) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Sep 28 2025 *)

Prog

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

Crossrefs

Cf. A002294, A365178, A365180, A365182, A365183.

Sequence in context: A364747 A053157 A102231 * A367281 A127089 A241769

Adjacent sequences: A365178 A365179 A365180 * A365182 A365183 A365184

Keyword

nonn

Author

Seiichi Manyama, Aug 25 2023

Status

approved