A112703 - OEIS

%I #9 Jun 22 2016 12:40:12

%S 1,10,172,3817,95671,2575729,72725941,2124619642,63681430672,

%T 1947319848190,60511350647386,1905278320822060,60654011063307832,

%U 1949006134928921932,63131614948174818772,2059214227480322203177

%N Partial sum of Catalan numbers A000108 multiplied by powers of 9.

%H Harvey P. Dale, <a href="/A112703/b112703.txt">Table of n, a(n) for n = 0..645</a>

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

%F 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.

%F 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

%t Accumulate[Table[CatalanNumber[n]9^n,{n,0,20}]] (* _Harvey P. Dale_, Jun 22 2016 *)

%Y Tenth column (m=9) of triangle A112705.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Oct 31 2005