A390921 Expansion of 1/((1-x) * sqrt(1-12*x)).

1, 7, 61, 601, 6271, 67507, 741103, 8246887, 92686957, 1049674417, 11959331461, 136924493965, 1574023862761, 18155939656561, 210032393841961, 2435799262392601, 28310339109293791, 329672626737907651, 3845565982405069351, 44926004138095063951, 525567130559668000771

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..928

Formula

a(n) = Sum_{k=0..n} 3^k * binomial(2*k,k).

n*a(n) = (13*n-6)*a(n-1) - 6*(2*n-1)*a(n-2).

a(n) = a(n-1) + A098658(n).

Prog

(PARI) a(n) = sum(k=0, n, 3^k*binomial(2*k, k));

Crossrefs

Cf. A014882, A098405.

Cf. A000984, A098658.

Sequence in context: A098659 A269731 A199686 * A113718 A177132 A364430

Adjacent sequences: A390918 A390919 A390920 * A390922 A390923 A390924

Keyword

nonn

Author

Seiichi Manyama, Nov 24 2025

Status

approved