A364597 G.f. satisfies A(x) = 1/(1-x) + x^3*(1-x)*A(x)^5.

1, 1, 1, 2, 5, 11, 26, 71, 197, 540, 1521, 4401, 12826, 37597, 111385, 332861, 1000181, 3021071, 9174308, 27987989, 85712801, 263438881, 812394661, 2512807846, 7793552386, 24233089051, 75526196851, 235897169106, 738271145577, 2314825565700, 7270693111431

Offset

0,4

Links

Table of n, a(n) for n=0..30.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(n,3*k) * binomial(5*k,k) / (4*k+1).

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(n, 3*k)*binomial(5*k, k)/(4*k+1));

Crossrefs

Cf. A364595, A364596.

Sequence in context: A319760 A343872 A000664 * A242766 A182580 A067922

Adjacent sequences: A364594 A364595 A364596 * A364598 A364599 A364600

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 29 2023

Status

approved