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The digital root (A010888) of the Catalan numbers A000108.
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%I #14 Nov 28 2022 09:59:39

%S 1,1,2,5,5,6,6,6,8,2,2,7,4,4,9,9,9,6,6,6,3,3,3,9,9,9,8,2,2,4,1,1,3,3,

%T 3,1,7,7,2,5,5,9,9,9,9,9,9,9,9,9,9,9,9,6,6,6,3,3,3,9,9,9,3,3,3,6,6,6,

%U 9,9,9,9,9,9,9,9,9,9,9,9,8,2,2,4,1,1,3

%N The digital root (A010888) of the Catalan numbers A000108.

%H Nathaniel Johnston, <a href="/A130856/b130856.txt">Table of n, a(n) for n = 0..10000</a>

%p A130856 := proc(n) option remember: if(n=0)then return 1:fi: return ((add(procname(k)*procname(n-1-k),k=0..n-1)-1) mod 9) + 1 end: seq(A130856(n),n=0..100); # _Nathaniel Johnston_, May 05 2011

%t droot[n_]:=NestWhile[Total[IntegerDigits[#]]&,n,#>9&]; droot/@CatalanNumber[ Range[ 0,100]] (* _Harvey P. Dale_, Apr 09 2022 *)

%o (PARI) a(n) = (binomial(2*n,n)/(n+1)-1)%9 + 1; \\ _Michel Marcus_, Nov 28 2022

%Y Cf. A000108, A010888, A130851.

%K nonn,easy,base

%O 0,3

%A _N. J. A. Sloane_, Aug 21 2007

%E Name corrected by _Nathaniel Johnston_, May 05 2011