A390137 Expansion of 1/((1-5*x) * sqrt(1+4*x)).

1, 3, 21, 85, 495, 2223, 12039, 56763, 296685, 1434805, 7358781, 36088473, 183146521, 905332005, 4566776625, 22678765605, 113994908415, 567640935855, 2847279814575, 14201053809075, 71143115574195, 355177319996535, 1777990698946395, 8881720064004375, 44440847923704975

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

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

n*a(n) = (n+2)*a(n-1) + 10*(2*n-1)*a(n-2).

a(n) = 5*a(n-1) + (-1)^n * A000984(n).

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*5^(n-k)*binomial(2*k, k));

Crossrefs

Cf. A000984, A091520, A144635.

Sequence in context: A112851 A253943 A034490 * A071351 A083231 A129755

Adjacent sequences: A390134 A390135 A390136 * A390138 A390139 A390140

Keyword

nonn

Author

Seiichi Manyama, Nov 24 2025

Status

approved