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A082852 a(0)=0, a(n) = A014137(A072643(n)-1).

%I A082852 #11 Jan 11 2024 13:10:56
%S A082852 0,1,2,2,4,4,4,4,4,9,9,9,9,9,9,9,9,9,9,9,9,9,9,23,23,23,23,23,23,23,
%T A082852 23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,
%U A082852 23,23,23,23,23,23,23,23,23,23,23,23,65,65,65,65,65,65,65,65,65,65,65,65
%N A082852 a(0)=0, a(n) = A014137(A072643(n)-1).
%C A082852 A014137(n) occurs A000108(n+1) times.
%t A082852 a014137[n_] := Sum[CatalanNumber[k], {k, 0, n}];
%t A082852 a072643[n_] := Module[{i, c, a}, i = c = 0; a = 1; While[n > c, a *= (4*i + 2)/(i + 2); i++; c += a]; i];
%t A082852 a[n_] := a014137[a072643[n] - 1];
%t A082852 Table[a[n], {n, 0, 76}] (* _Jean-François Alcover_, Dec 26 2017 *)
%o A082852 (Scheme) (define (A082852 n) (if (zero? n) 0 (A014137 (-1+ (A072643 n)))))
%o A082852 (Sage)
%o A082852 def A082852(n) :
%o A082852     i = c = 0; a = 1
%o A082852     while n > c :
%o A082852         a *= (4*i+2)/(2+i)
%o A082852         i += 1; c += a
%o A082852     return c-a+1
%o A082852 [A082852(n) for n in (0..76)] # - _Peter Luschny_, Sep 07 2012
%Y A082852 Used to compute A082853. Cf. also A082855.
%K A082852 nonn
%O A082852 0,3
%A A082852 _Antti Karttunen_, Apr 17 2003