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A258412 Decimal expansion of Integral_{x=0..1} Product_{k>=1} (1-x^k)^k dx.

%I A258412 #19 Oct 10 2023 09:20:19
%S A258412 2,9,8,7,8,3,3,6,5,1,0,6,5,6,7,2,9,8,7,7,0,9,5,3,7,7,2,1,1,4,0,0,7,0,
%T A258412 9,7,3,6,0,9,2,1,8,2,5,2,5,0,1,4,7,4,3,3,4,9,0,4,5,1,1,7,4,9,9,1,7,8,
%U A258412 0,5,0,0,4,8,9,6,7,4,3,5,2,2,0,5,8,1,0,5,0,9,8,7,2,2,4,0,2,6,3,5,0,7,6,1,6,4
%N A258412 Decimal expansion of Integral_{x=0..1} Product_{k>=1} (1-x^k)^k dx.
%C A258412 Integral_{x=0..1} Product_{k=1..n} (1+x^k)^k dx ~ 3*2^(n*(n+1)/2 + 1)/n^3.
%C A258412 Integral_{x=0..1} Product_{k=1..n} (1+x^k)   dx ~ 2^(n+2)/n^2.
%C A258412 Integral_{x=0..1} Product_{k>=1}   (1-x^k)   dx = A258232 = 0.3684125359314...
%C A258412 Integral_{x=0..1} Product_{k=1..n} (1-x^k)^n dx ~ 1/n.
%C A258412 Integral_{x=0..1} Product_{k=1..n} (1+x^k)^n dx ~ 2^(n^2 + 2)/n^3.
%H A258412 Vaclav Kotesovec, <a href="http://oeis.org/A258232/a258232_2.pdf">The integration of q-series</a>
%e A258412 0.298783365106567298770953772114...
%Y A258412 Cf. A073592, A258232.
%K A258412 nonn,cons
%O A258412 0,1
%A A258412 _Vaclav Kotesovec_, May 29 2015
%E A258412 More digits from _Vaclav Kotesovec_, Oct 10 2023