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A258229 Numerator of Integral_{x=0..1} Product_{k=1..n} (1-x^k) dx.

%I A258229 #11 May 24 2015 08:47:13
%S A258229 1,5,41,188,20777,126661,375407075,4551271607,2186878968457691,
%T A258229 405572061653677013,579868609560670025014303,
%U A258229 756499881167742750802544581,90137667815984749912207449629,12095883009361301429642260272492831583,83142433646555338064479023776802561123293
%N A258229 Numerator of Integral_{x=0..1} Product_{k=1..n} (1-x^k) dx.
%C A258229 Limit n->infinity a(n) / A258230(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 A258229 Vaclav Kotesovec, <a href="/A258229/b258229.txt">Table of n, a(n) for n = 1..69</a>
%H A258229 StackExchange - Mathematica, <a href="http://mathematica.stackexchange.com/questions/38919/no-response-to-an-infinite-limit">No response to an infinite limit</a>
%e A258229 Product_{k=1..n} (1-x^k)
%e A258229 n=1 1 - x
%e A258229 n=2 1 - x - x^2 + x^3
%e A258229 n=3 1 - x - x^2 + x^4 + x^5 - x^6
%e A258229 Integral Product_{k=1..n} (1-x^k) dx
%e A258229 n=1 x - x^2/2
%e A258229 n=2 x - x^2/2 - x^3/3 + x^4/4
%e A258229 n=3 x - x^2/2 - x^3/3 + x^5/5 + x^6/6 - x^7/7
%e A258229 For Integral_{x=0..1} set x=1
%e A258229 n=1 1 - 1/2 = 1/2, a(1) = 1
%e A258229 n=2 1 - 1/2 - 1/3 + 1/4 = 5/12, a(2) = 5
%e A258229 n=3 1 - 1/2 - 1/3 + 1/5 + 1/6 - 1/7 = 41/105, a(3) = 41
%t A258229 nmax=15; p=1; Table[p=Expand[p*(1-x^n)]; Total[CoefficientList[p,x]/Range[1,Exponent[p,x]+1]], {n,1,nmax}] // Numerator
%Y A258229 Cf. A258230, A258191, A258192, A258232.
%K A258229 nonn
%O A258229 1,2
%A A258229 _Vaclav Kotesovec_, May 24 2015