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A258406 Decimal expansion of Integral_{x=0..1} Product_{k>=1} (1-x^k)^2 dx.

%I A258406 #14 Oct 10 2023 07:53:36
%S A258406 2,5,3,8,7,4,0,8,2,3,7,8,2,7,6,0,0,2,9,8,8,5,0,8,8,9,3,8,1,6,3,3,2,9,
%T A258406 1,2,3,8,4,7,6,3,6,3,4,3,1,9,3,3,1,3,5,1,4,7,5,6,0,6,7,6,0,5,8,8,6,9,
%U A258406 6,6,3,0,9,2,7,3,5,4,6,9,1,6,8,5,9,8,1,6,6,0,3,1,4,9,6,8,3,7,8,6,5,4,1,2,5,0
%N A258406 Decimal expansion of Integral_{x=0..1} Product_{k>=1} (1-x^k)^2 dx.
%H A258406 Vaclav Kotesovec, <a href="http://oeis.org/A258232/a258232_2.pdf">The integration of q-series</a>
%F A258406 Equals Sum_{n>=0} Sum_{k=0..n} 8*(n+1)*(-1)^n / ((n^2 - 2*k^2 + 2*k*n + n + 2) * (n^2 - 2*k^2 + 2*k*n + 5*n + 6)).
%F A258406 Equals Sum_{n>=0} Sum_{j=-floor(n/2)..floor(n/2)} (-1)^(n+j) / (n*(n+1)/2 - j*(3*j-1)/2 + 1).
%e A258406 0.2538740823782760029885088938163329123847636343193313514756067...
%p A258406 evalf(Sum(Sum(8*(n+1)*(-1)^n / ((n^2 - 2*k^2 + 2*k*n + n + 2) * (n^2 - 2*k^2 + 2*k*n + 5*n + 6)), k=0..n), n=0..infinity), 120);
%t A258406 RealDigits[NIntegrate[QPochhammer[x]^2, {x, 0, 1}, WorkingPrecision -> 120], 10, 106][[1]] (* _Vaclav Kotesovec_, Oct 10 2023 *)
%Y A258406 Cf. A002107, A258232, A258407, A258404, A258405.
%K A258406 nonn,cons
%O A258406 0,1
%A A258406 _Vaclav Kotesovec_, May 29 2015