login
Denominator of b(n) = Sum_{k=1..n} (-1)^(k+1)/k*Sum_{i=0..k-1} (-1)^i/(2*i+1).
2

%I #10 May 05 2022 07:28:05

%S 1,3,45,315,1575,51975,4729725,4729725,18555075,4583103525,

%T 50414138775,1159525191825,793359341775,15073827493725,

%U 2185704986590125,67756854584293875,1151866527932995875,3455599583798987625,2429286507410688300375,2429286507410688300375

%N Denominator of b(n) = Sum_{k=1..n} (-1)^(k+1)/k*Sum_{i=0..k-1} (-1)^i/(2*i+1).

%H Amiram Eldar, <a href="/A073595/b073595.txt">Table of n, a(n) for n = 1..772</a>

%F Limit_{n -> infinity} b(n) = G, the Catalan constant (A006752).

%t Denominator[Accumulate[Table[(-1)^(k + 1)/k * Sum[(-1)^i/(2*i + 1), {i, 0, k - 1}], {k, 1, 20}]]] (* _Amiram Eldar_, May 05 2022 *)

%o (PARI) a(n)=denominator(sum(k=1,n,(-1)^(k+1)/k*sum(i=0,k-1,(-1)^i/(2*i+1))))

%Y Cf. A006752, A073594 (numerators).

%K easy,frac,nonn

%O 1,2

%A _Benoit Cloitre_, Aug 28 2002