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%I #30 Sep 03 2017 03:21:41
%S 2,4,5,13,19,58,191,131,1187,2231,17519,71063,29881,323423,2887921,
%T 13237457,2397389,15030317,742458253,3748521653,9670072483,
%U 25451905333,10932619111,78684575461,4163946939067,11799518538967,136025604432743,159359728522979
%N a(n) = denominator of 1/(1 + 1/(1 + 2/(1 + ... (1 + n)))).
%H Seiichi Manyama, <a href="/A289491/b289491.txt">Table of n, a(n) for n = 1..843</a>
%H OEIS Wiki, <a href="/wiki/A_remarkable_formula_of_Ramanujan">A remarkable formula of Ramanujan</a>
%F a(n) = A225435(n) + A225436(n).
%F A225436(n)/a(n) = 1/(1 + 1/(1 + 2/(1 + ... (1 + n)))) = A000932(n)/A000085(n+1).
%e 1/2, 3/4, 3/5, 9/13, 12/19, 39/58, 123/191, 87/131, 771/1187, 1473/2231, 11427/17519, 46779/71063, 19533/29881, ... = A225436/A289491 -> A108088.
%e A225436(1)/a(1) = 1/2 = 1/(1 + 1) = 1/2,
%e A225436(2)/a(2) = 3/4 = 1/(1 + 1/(1 + 2)) = 3/4,
%e A225436(3)/a(3) = 3/5 = 1/(1 + 1/(1 + 2/(1 + 3))) = 6/10,
%e A225436(4)/a(4) = 9/13 = 1/(1 + 1/(1 + 2/(1 + 3/(1 + 4)))) = 18/26.
%p p:= (i, n)-> `if`(i=n, (1+n), 1+i/p(i+1,n)):
%p a:= n-> denom(1/p(1,n)):
%p seq(a(n), n=1..30); # _Alois P. Heinz_, Sep 02 2017
%Y Cf. A000085, A000932, A108088, A225435, A225436 (numerators).
%K nonn,frac
%O 1,1
%A _Seiichi Manyama_, Sep 02 2017
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