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

Author

Wolfdieter Lang, Oct 31 2005

Keywords

• nonn
• easy

Crossrefs

Column m=8 of triangle A112705.

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