A112702 - OEIS

%I #8 Jan 30 2024 16:18:06

%S 1,9,137,2697,60041,1436297,36039305,935717513,24927136393,

%T 677493729929,18712061405833,523679956331145,14818155751139977,

%U 423231749888535177,12185543261045516937,353292577084597987977,10305591916877658319497

%N Partial sum of Catalan numbers A000108 multiplied by powers of 8.

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

%F 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.

%F 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

%Y Column m=8 of triangle A112705.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Oct 31 2005