A258191 - OEIS

%I #14 Jun 09 2015 10:40:13

%S 1,11,293,487,129952159,13084761625,8277192566411,576489266167410341,

%T 2154341459717480222819111,1562388737113054944319018297,

%U 4507453407946726622146977923716952747,46170199302621715634236277404186409941,20107953791404084220109855379873778475523352268948164789

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

%C Limit n->infinity (a(n)/A258192(n))^(1/n) = 0.185155...

%C The limit is equal to 0.1851552893223595946473132111979542852738... = 1/5.400871904118154152466091119104270052029... (see A258234). - _Vaclav Kotesovec_, May 24 2015

%H Vaclav Kotesovec, <a href="/A258191/b258191.txt">Table of n, a(n) for n = 1..50</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} x^k*(1-x^k)

%e n=1 x - x^2

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

%e n=3 x^6 - x^7 - x^8 + x^10 + x^11 - x^12

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

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

%e n=2 x^4/4 - x^5/5 - x^6/6 + x^7/7

%e n=3 x^7/7 - x^8/8 - x^9/9 + x^11/11 + x^12/12 - x^13/13

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

%e n=1 1/2 - 1/3 = 1/6, a(1)=1

%e n=2 1/4 - 1/5 - 1/6 + 1/7 = 11/420, a(2)=11

%e n=3 1/7 - 1/8 - 1/9 + 1/11 + 1/12 - 1/13 = 293/72072, a(3)=293

%t 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}] // Numerator

%Y Cf. A258192, A258229, A258230, A258234.

%K nonn

%O 1,2

%A _Vaclav Kotesovec_, May 23 2015