login
A112702
Partial sum of Catalan numbers A000108 multiplied by powers of 8.
0
1, 9, 137, 2697, 60041, 1436297, 36039305, 935717513, 24927136393, 677493729929, 18712061405833, 523679956331145, 14818155751139977, 423231749888535177, 12185543261045516937, 353292577084597987977, 10305591916877658319497
OFFSET
0,2
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
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 31 2005
STATUS
approved