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%I #13 Sep 26 2022 08:00:12
%S 2,5,53,9886302,32706124785400851,
%T 105840083750427500921760353826840828183,
%U 51348043200265516352304296553233166994035195487912155511387668758325728717007499617
%N a(n) = denominator of Sum_{k=1..n} 1/A134473(k).
%C The numerator of Sum_{k=1..n} 1/A134473(k) is A134474(n). A134474(n)/A134475(n) approaches a constant (0.6037789...) as n approaches infinity.
%p Digits := 220 ; A134473 := proc(n) option remember ; local su,mu ; if n =1 then 2; else su := add(1/procname(k),k=1..n-1) ; mu := mul(1/(1+1/procname(j)),j=1..n-1) ; ceil( (1+su+sqrt((su-1)^2+4*mu))/2/(mu-su) ) ; fi; end: A134475 := proc(n) add(1/A134473(k),k=1..n) ; denom(%) ; end: seq(A134475(n),n=1..9) ; # _R. J. Mathar_, Jul 20 2009
%t b[n_] := b[n] = If[n == 1, 2, With[{x = Product[1/(1 + 1/b[j]), {j, 1, n-1}], y = Sum[1/b[j], {j, 1, n-1}]}, Ceiling[(1 + y + Sqrt[(y-1)^2 + 4 x])/(2 (x-y))]]];
%t a[n_] := Sum[1/b[k], {k, 1, n}] // Denominator;
%t Table[a[n], {n, 1, 7}] (* _Jean-François Alcover_, Sep 26 2022 *)
%Y Cf. A134473, A134474, A134476, A134477.
%K frac,nonn
%O 1,1
%A _Leroy Quet_, Oct 27 2007
%E More terms from _R. J. Mathar_, Jul 20 2009
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