A364827 G.f. satisfies A(x) = 1 - x*A(x)^5 * (1 - 3*A(x)).

1, 2, 26, 478, 10254, 240122, 5950530, 153417542, 4072868742, 110585691634, 3056671795946, 85722961493742, 2433127206219582, 69763483031049066, 2017643094336224914, 58789801741123032918, 1724199860717303739062, 50858327392484088101346

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..666

Formula

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

a(n) = (1/n) * Sum_{k=0..n-1} 2^(n-k) * binomial(n,k) * binomial(6*n-k,n-1-k) for n > 0.

a(n) = (1/n) * Sum_{k=1..n} 2^k * 3^(n-k) * binomial(n,k) * binomial(5*n,k-1) for n > 0.

Prog

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

Crossrefs

Cf. A025192, A107841, A235347, A364825, A364826.

Cf. A243668, A363006.

Sequence in context: A285026 A137100 A228411 * A371700 A364196 A216254

Adjacent sequences: A364824 A364825 A364826 * A364828 A364829 A364830

Keyword

nonn

Author

Seiichi Manyama, Aug 09 2023

Status

approved