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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 October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)