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A112703 Partial sum of Catalan numbers A000108 multiplied by powers of 9. 1
1, 10, 172, 3817, 95671, 2575729, 72725941, 2124619642, 63681430672, 1947319848190, 60511350647386, 1905278320822060, 60654011063307832, 1949006134928921932, 63131614948174818772, 2059214227480322203177 (list; graph; refs; listen; history; text; internal format)
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: A187204 A133273 A239763 * A132676 A270958 A200574

Adjacent sequences:  A112700 A112701 A112702 * A112704 A112705 A112706

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 31 2005

STATUS

approved

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Last modified March 20 21:49 EDT 2019. Contains 321352 sequences. (Running on oeis4.)