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A258192 Denominator of Integral_{x=0..1} Product_{k=1..n} x^k*(1-x^k) dx.

%I A258192 #14 Jun 09 2015 10:40:24
%S A258192 6,420,72072,760760,1266697832400,783333734619744,3002950101013562700,
%T A258192 1253414030788528596187200,27809824888100301666382826331840,
%U A258192 118802724769051077369996224554510800,2005396188718644499811084404372455793370133120
%N A258192 Denominator of Integral_{x=0..1} Product_{k=1..n} x^k*(1-x^k) dx.
%C A258192 Limit n->infinity (A258191(n)/a(n))^(1/n) = 0.185155...
%C A258192 The limit is equal to 0.1851552893223595946473132111979542852738... = 1/5.400871904118154152466091119104270052029... (see A258234). - _Vaclav Kotesovec_, May 24 2015
%H A258192 Vaclav Kotesovec, <a href="/A258192/b258192.txt">Table of n, a(n) for n = 1..49</a>
%H A258192 StackExchange - Mathematica, <a href="http://mathematica.stackexchange.com/questions/38919/no-response-to-an-infinite-limit">No response to an infinite limit</a>
%e A258192 Product_{k=1..n} x^k*(1-x^k)
%e A258192 n=1 x - x^2
%e A258192 n=2 x^3 - x^4 - x^5 + x^6
%e A258192 n=3 x^6 - x^7 - x^8 + x^10 + x^11 - x^12
%e A258192 Integral Product_{k=1..n} x^k*(1-x^k) dx
%e A258192 n=1 x^2/2 - x^3/3
%e A258192 n=2 x^4/4 - x^5/5 - x^6/6 + x^7/7
%e A258192 n=3 x^7/7 - x^8/8 - x^9/9 + x^11/11 + x^12/12 - x^13/13
%e A258192 For Integral_{x=0..1} set x=1
%e A258192 n=1 1/2 - 1/3 = 1/6, a(1)=6
%e A258192 n=2 1/4 - 1/5 - 1/6 + 1/7 = 11/420, a(2)=420
%e A258192 n=3 1/7 - 1/8 - 1/9 + 1/11 + 1/12 - 1/13 = 293/72072, a(3)=72072
%t A258192 nmax=15; p=1; Table[p=Expand[p*x^n*(1-x^n)]; Total[CoefficientList[p,x]/Range[1,Exponent[p,x]+1]], {n,1,nmax}] // Denominator
%Y A258192 Cf. A258191, A258229, A258230, A258234.
%K A258192 nonn
%O A258192 1,1
%A A258192 _Vaclav Kotesovec_, May 23 2015