A365180 G.f. satisfies A(x) = 1 + x*A(x)^4*(1 + x*A(x)).

1, 1, 5, 31, 223, 1740, 14328, 122549, 1078197, 9695359, 88710199, 823247686, 7730244098, 73310150097, 701163085849, 6755544043969, 65506554804129, 638794412442172, 6260571309256152, 61632794482411367, 609197871548209907, 6043456939539775056

Offset

0,3

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A002294, A365178, A365181, A365182, A365183.

Cf. A364747.

Sequence in context: A199877 A058309 A226924 * A192950 A001910 A052773

Adjacent sequences: A365177 A365178 A365179 * A365181 A365182 A365183

Keyword

nonn

Author

Seiichi Manyama, Aug 25 2023

Status

approved