A364748 G.f. A(x) satisfies A(x) = 1 + x*A(x)^5 / (1 - x*A(x)).

1, 1, 6, 47, 424, 4159, 43097, 464197, 5145475, 58313310, 672598269, 7869856070, 93183973405, 1114471042413, 13443614108307, 163372291277764, 1998239045199623, 24580340878055298, 303893356012560280, 3774099648814193998, 47061518776483143441

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..890

Formula

a(n) = (1/n) * Sum_{k=0..n-1} binomial(n,k) * binomial(5*n-4*k,n-1-k) for n > 0.

From Seiichi Manyama, Dec 05 2024: (Start)

G.f. A(x) satisfies A(x) = 1/(1 - x*A(x)^4/(1 - x*A(x))).

If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(n+(s-1)*k-1,n-k)/(t*k+u*(n-k)+r). (End)

Prog

(PARI) a(n) = if(n==0, 1, sum(k=0, n-1, binomial(n, k)*binomial(5*n-4*k, n-1-k))/n);
(PARI) a(n, r=1, s=1, t=5, u=1) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r)); \\ Seiichi Manyama, Dec 05 2024

Crossrefs

Cf. A000108, A001003, A108447, A364747, A378691, A378692.

Cf. A002295, A243667, A365192, A365193, A365194.

Sequence in context: A341927 A071878 A369502 * A365186 A104256 A289211

Adjacent sequences: A364745 A364746 A364747 * A364749 A364750 A364751

Keyword

nonn

Author

Seiichi Manyama, Aug 05 2023

Status

approved