A365183 G.f. satisfies A(x) = 1 + x*A(x)^4*(1 + x*A(x)^4).

1, 1, 5, 34, 268, 2299, 20838, 196326, 1903524, 18868861, 190356231, 1948055058, 20173907384, 211020478270, 2226243632838, 23660868061422, 253099278807684, 2722819049879436, 29439894433161189, 319749417998303470, 3486914150183526920

Offset: 0

Author

Seiichi Manyama, Aug 25 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..939
• Jun Yan, Lattice paths enumerations weighted by ascent lengths, arXiv:2501.01152 [math.CO], 2025. See p. 13.

Crossrefs

Cf. A002294, A365178, A365180, A365181, A365182.

Cf. A006605, A255673, A365189.

Cf. A364989.

Programs

PARI

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

Formula

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