A365192 G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 - x*A(x)^2).

1, 1, 6, 48, 443, 4445, 47107, 518835, 5880223, 68130860, 803369481, 9609294542, 116310009888, 1421951861817, 17533301767624, 217796367181117, 2722942699583650, 34236790400004432, 432649744252128084, 5492060945760586212, 69998993052214823013

Offset: 0

Author

Seiichi Manyama, Aug 25 2023

Keywords

• nonn

Crossrefs

Cf. A002295, A243667, A349332, A364748, A365193, A365194.

Cf. A365186.

Programs

PARI

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

Formula

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