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Denominator of Integral_{x=0..1} Product_{k=1..n} (1-x^k) dx.
5

%I #12 May 24 2015 12:28:13

%S 2,12,105,495,55440,340340,1012647636,12304749600,5920545668637600,

%T 1098951951860282520,1572101004939647757775200,

%U 2051717579526635495717258016,244523633377266327241371614400,32818916025992059215981780272862841200

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

%C 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 Vaclav Kotesovec, <a href="/A258230/b258230.txt">Table of n, a(n) for n = 1..69</a>

%H StackExchange - Mathematica, <a href="http://mathematica.stackexchange.com/questions/38919/no-response-to-an-infinite-limit">No response to an infinite limit</a>

%e Product_{k=1..n} (1-x^k)

%e n=1 1 - x

%e n=2 1 - x - x^2 + x^3

%e n=3 1 - x - x^2 + x^4 + x^5 - x^6

%e Integral Product_{k=1..n} (1-x^k) dx

%e n=1 x - x^2/2

%e n=2 x - x^2/2 - x^3/3 + x^4/4

%e n=3 x - x^2/2 - x^3/3 + x^5/5 + x^6/6 - x^7/7

%e For Integral_{x=0..1} set x=1

%e n=1 1 - 1/2 = 1/2, a(1) = 2

%e n=2 1 - 1/2 - 1/3 + 1/4 = 5/12, a(2) = 12

%e n=3 1 - 1/2 - 1/3 + 1/5 + 1/6 - 1/7 = 41/105, a(3) = 105

%t 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 Cf. A258229, A258191, A258192, A258232.

%K nonn

%O 1,1

%A _Vaclav Kotesovec_, May 24 2015