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A375791 a(n) = A375516(n+1) / A375516(n).

%I A375791 #16 Jul 02 2025 03:45:04
%S A375791 2,2,3,4,25,201,40201,1212060151,1305857607493406801,
%T A375791 1534737681943564047120326770001682121,
%U A375791 11777098761887521784975815904636471022877972047160405176265171997646882601
%N A375791 a(n) = A375516(n+1) / A375516(n).
%H A375791 Alois P. Heinz, <a href="/A375791/b375791.txt">Table of n, a(n) for n = 0..14</a>
%e A375791 a(7) = A375516(8) / A375516(7) = 11752718467440661200 / 9696481200 = 1212060151.
%p A375791 s:= proc(n) s(n):= `if`(n=0, 0, s(n-1)+1/(n*b(n))) end:
%p A375791 b:= proc(n) b(n):= 1+floor(1/((1-s(n-1))*n)) end:
%p A375791 a:= n-> denom(s(n+1))/denom(s(n)):
%p A375791 seq(a(n), n=0..10);  # _Alois P. Heinz_, Oct 19 2024
%t A375791 s[n_] := s[n] = If[n == 0, 0, s[n-1] + 1/(n*b[n])];
%t A375791 b[n_] := b[n] = 1 + Floor[1/((1 - s[n-1])*n)];
%t A375791 a[n_] := Denominator[s[n+1]]/Denominator[s[n]];
%t A375791 Table[a[n], {n, 0, 10}] (* _Jean-François Alcover_, Jul 02 2025, after _Alois P. Heinz_ *)
%o A375791 (PARI) { r = 1; for (n = 1, 11, a = floor(1/(r*n))+1; d = denominator(r); r -= 1/(n*a); print1 (denominator(r)/d", ");); }
%o A375791 (Python)
%o A375791 from itertools import count, islice
%o A375791 from math import gcd
%o A375791 def A375791_gen(): # generator of terms
%o A375791     p, q = 0, 1
%o A375791     for k in count(1):
%o A375791         m = q//(k*(q-p))+1
%o A375791         p, q = p*k*m+q, k*m*q
%o A375791         p //= (r:=gcd(p,q))
%o A375791         q //= r
%o A375791         yield k*m//r
%o A375791 A375791_list = list(islice(A375791_gen(),11)) # _Chai Wah Wu_, Aug 30 2024
%Y A375791 Cf. A374663, A375516.
%K A375791 nonn
%O A375791 0,1
%A A375791 _Rémy Sigrist_ and _N. J. A. Sloane_, Aug 29 2024