A365188 G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x*A(x)^4).

1, 1, 6, 49, 465, 4807, 52533, 596936, 6981798, 83497115, 1016367737, 12550853210, 156845913315, 1979870172453, 25207383853375, 323325558146400, 4174108907656633, 54195445136831670, 707225283913589280, 9270735916525207605, 122020617365557674605

Offset: 0

Author

Seiichi Manyama, Aug 25 2023

Keywords

• nonn

Crossrefs

Cf. A002295, A365184, A365185, A365186, A365187, A365189.

Cf. A243667.

Programs

PARI

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

Formula

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