A390923 Expansion of 1/((1-3*x) * sqrt(1-8*x)).

1, 7, 45, 295, 2005, 14079, 101373, 743415, 5524965, 41468335, 313595149, 2385510183, 18232753525, 139899975775, 1076970301725, 8313801800535, 64333809840645, 498871863989775, 3875607860052525, 30157921247331975, 235016325545956245, 1833857554535463615

Offset

0,2

Links

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

Formula

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

n*a(n) = (11*n-4)*a(n-1) - 12*(2*n-1)*a(n-2).

a(n) = 3*a(n-1) + A059304(n).

Prog

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

Crossrefs

Cf. A000984, A059304, A132310.

Sequence in context: A062274 A182556 A363570 * A219020 A280597 A301319

Adjacent sequences: A390920 A390921 A390922 * A390924 A390925 A390926

Keyword

nonn

Author

Seiichi Manyama, Nov 24 2025

Status

approved