A390924 Expansion of 1/((1-2*x) * sqrt(1-12*x)).

1, 8, 70, 680, 7030, 75296, 824188, 9154160, 102748390, 1162484240, 13234625524, 151434413552, 1739968195900, 20061852185600, 232000158556600, 2689767185663840, 31254074218228870, 363870436065071600, 4243634227797304900, 49567706611284604400, 579776539644142145620

Offset

0,2

Links

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

Formula

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

n*a(n) = (14*n-6)*a(n-1) - 12*(2*n-1)*a(n-2).

a(n) = 2*a(n-1) + A098658(n).

Prog

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

Crossrefs

Cf. A000984, A082590, A098658, A390921.

Sequence in context: A299938 A152263 A142986 * A123511 A322416 A287482

Adjacent sequences: A390921 A390922 A390923 * A390925 A390926 A390927

Keyword

nonn

Author

Seiichi Manyama, Nov 24 2025

Status

approved