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A258230 Denominator of Integral_{x=0..1} Product_{k=1..n} (1-x^k) dx.

%I A258230 #12 May 24 2015 12:28:13
%S A258230 2,12,105,495,55440,340340,1012647636,12304749600,5920545668637600,
%T A258230 1098951951860282520,1572101004939647757775200,
%U A258230 2051717579526635495717258016,244523633377266327241371614400,32818916025992059215981780272862841200
%N A258230 Denominator of Integral_{x=0..1} Product_{k=1..n} (1-x^k) dx.
%C A258230 Limit n->infinity A258229(n) / a(n) = limit n->infinity Integral_{x=0..1} Product_{k=1..n} (1-x^k) dx = 8*sqrt(3/23)*Pi*sinh(sqrt(23)*Pi/6) / (2*cosh(sqrt(23)*Pi/3)-1) = A258232 = 0.368412535931433652321316597327851...
%H A258230 Vaclav Kotesovec, <a href="/A258230/b258230.txt">Table of n, a(n) for n = 1..69</a>
%H A258230 StackExchange - Mathematica, <a href="http://mathematica.stackexchange.com/questions/38919/no-response-to-an-infinite-limit">No response to an infinite limit</a>
%e A258230 Product_{k=1..n} (1-x^k)
%e A258230 n=1 1 - x
%e A258230 n=2 1 - x - x^2 + x^3
%e A258230 n=3 1 - x - x^2 + x^4 + x^5 - x^6
%e A258230 Integral Product_{k=1..n} (1-x^k) dx
%e A258230 n=1 x - x^2/2
%e A258230 n=2 x - x^2/2 - x^3/3 + x^4/4
%e A258230 n=3 x - x^2/2 - x^3/3 + x^5/5 + x^6/6 - x^7/7
%e A258230 For Integral_{x=0..1} set x=1
%e A258230 n=1 1 - 1/2 = 1/2, a(1) = 2
%e A258230 n=2 1 - 1/2 - 1/3 + 1/4 = 5/12, a(2) = 12
%e A258230 n=3 1 - 1/2 - 1/3 + 1/5 + 1/6 - 1/7 = 41/105, a(3) = 105
%t A258230 nmax=15; p=1; Table[p=Expand[p*(1-x^n)]; Total[CoefficientList[p,x]/Range[1,Exponent[p,x]+1]], {n,1,nmax}] // Denominator
%Y A258230 Cf. A258229, A258191, A258192, A258232.
%K A258230 nonn
%O A258230 1,1
%A A258230 _Vaclav Kotesovec_, May 24 2015