A258191 Numerator of Integral_{x=0..1} Product_{k=1..n} x^k*(1-x^k) dx.

1, 11, 293, 487, 129952159, 13084761625, 8277192566411, 576489266167410341, 2154341459717480222819111, 1562388737113054944319018297, 4507453407946726622146977923716952747, 46170199302621715634236277404186409941, 20107953791404084220109855379873778475523352268948164789

Offset: 1

Author

Vaclav Kotesovec, May 23 2015

Keywords

• nonn

Comments

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

The limit is equal to 0.1851552893223595946473132111979542852738... = 1/5.400871904118154152466091119104270052029... (see A258234). - Vaclav Kotesovec, May 24 2015

Examples

			Product_{k=1..n} x^k*(1-x^k)
n=1 x - x^2
n=2 x^3 - x^4 - x^5 + x^6
n=3 x^6 - x^7 - x^8 + x^10 + x^11 - x^12
Integral Product_{k=1..n} x^k*(1-x^k) dx
n=1 x^2/2 - x^3/3
n=2 x^4/4 - x^5/5 - x^6/6 + x^7/7
n=3 x^7/7 - x^8/8 - x^9/9 + x^11/11 + x^12/12 - x^13/13
For Integral_{x=0..1} set x=1
n=1 1/2 - 1/3 = 1/6, a(1)=1
n=2 1/4 - 1/5 - 1/6 + 1/7 = 11/420, a(2)=11
n=3 1/7 - 1/8 - 1/9 + 1/11 + 1/12 - 1/13 = 293/72072, a(3)=293
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..50
• StackExchange - Mathematica, No response to an infinite limit

Crossrefs

Cf. A258192, A258229, A258230, A258234.

Programs

Mathematica

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