A112703 Partial sum of Catalan numbers A000108 multiplied by powers of 9.

1, 10, 172, 3817, 95671, 2575729, 72725941, 2124619642, 63681430672, 1947319848190, 60511350647386, 1905278320822060, 60654011063307832, 1949006134928921932, 63131614948174818772, 2059214227480322203177

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..645

Formula

a(n)=sum(C(k)*9^k, k=0..n), n>=0, with C(n):=A000108(n).

G.f.: c(9*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) +(-37*n+17)*a(n-1) +18*(2*n-1)*a(n-2)=0. - R. J. Mathar, Jun 08 2016

Mathematica

Accumulate[Table[CatalanNumber[n]9^n, {n, 0, 20}]] (* Harvey P. Dale, Jun 22 2016 *)

Crossrefs

Tenth column (m=9) of triangle A112705.

Sequence in context: A346458 A133273 A239763 * A132676 A270958 A200574

Adjacent sequences: A112700 A112701 A112702 * A112704 A112705 A112706

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 31 2005

Status

approved