%I #12 Oct 19 2024 21:07:12
%S 2,2,3,4,25,201,40201,1212060151,1305857607493406801,
%T 1534737681943564047120326770001682121,
%U 11777098761887521784975815904636471022877972047160405176265171997646882601
%N a(n) = A375516(n+1) / A375516(n).
%H Alois P. Heinz, <a href="/A375791/b375791.txt">Table of n, a(n) for n = 0..14</a>
%e a(7) = A375516(8) / A375516(7) = 11752718467440661200 / 9696481200 = 1212060151.
%p s:= proc(n) s(n):= `if`(n=0, 0, s(n-1)+1/(n*b(n))) end:
%p b:= proc(n) b(n):= 1+floor(1/((1-s(n-1))*n)) end:
%p a:= n-> denom(s(n+1))/denom(s(n)):
%p seq(a(n), n=0..10); # _Alois P. Heinz_, Oct 19 2024
%o (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 (Python)
%o from itertools import count, islice
%o from math import gcd
%o def A375791_gen(): # generator of terms
%o p, q = 0, 1
%o for k in count(1):
%o m = q//(k*(q-p))+1
%o p, q = p*k*m+q, k*m*q
%o p //= (r:=gcd(p,q))
%o q //= r
%o yield k*m//r
%o A375791_list = list(islice(A375791_gen(),11)) # _Chai Wah Wu_, Aug 30 2024
%Y Cf. A374663, A375516.
%K nonn
%O 0,1
%A _Rémy Sigrist_ and _N. J. A. Sloane_, Aug 29 2024