A112702 Partial sum of Catalan numbers A000108 multiplied by powers of 8.

1, 9, 137, 2697, 60041, 1436297, 36039305, 935717513, 24927136393, 677493729929, 18712061405833, 523679956331145, 14818155751139977, 423231749888535177, 12185543261045516937, 353292577084597987977, 10305591916877658319497

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = Sum_{k=0..n} C(k)*8^k, with C(n) = A000108(n).

G.f.: c(8*x)/(1-x), where c(x) = (1-sqrt(1-4*x))/(2*x) is the o.g.f. of Catalan numbers A000108.

Conjecture: (n+1)*a(n) +3*(-11*n+5)*a(n-1) +16*(2*n-1)*a(n-2)=0. - R. J. Mathar, Jun 08 2016

Crossrefs

Column m=8 of triangle A112705.

Sequence in context: A156975 A081876 A139760 * A367426 A296394 A367246

Adjacent sequences: A112699 A112700 A112701 * A112703 A112704 A112705

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 31 2005

Status

approved