A365185 G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x*A(x)).

1, 1, 6, 46, 411, 3996, 41062, 438662, 4823133, 54221518, 620404859, 7201317005, 84590041441, 1003656037278, 12010861830069, 144804336388912, 1757106190680819, 21443109365898743, 263009775111233392, 3240530659303505547, 40088688455992604594

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

Prog

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

Crossrefs

Cf. A002295, A365184, A365186, A365187, A365188, A365189.

Cf. A364748.

Sequence in context: A084772 A199563 A349332 * A111531 A052781 A284109

Adjacent sequences: A365182 A365183 A365184 * A365186 A365187 A365188

Keyword

nonn

Author

Seiichi Manyama, Aug 25 2023

Status

approved