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

1, 5, 41, 188, 20777, 126661, 375407075, 4551271607, 2186878968457691, 405572061653677013, 579868609560670025014303, 756499881167742750802544581, 90137667815984749912207449629, 12095883009361301429642260272492831583, 83142433646555338064479023776802561123293

Offset: 1

Author

Vaclav Kotesovec, May 24 2015

Keywords

• nonn

Comments

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...

Examples

			Product_{k=1..n} (1-x^k)
n=1 1 - x
n=2 1 - x - x^2 + x^3
n=3 1 - x - x^2 + x^4 + x^5 - x^6
Integral Product_{k=1..n} (1-x^k) dx
n=1 x - x^2/2
n=2 x - x^2/2 - x^3/3 + x^4/4
n=3 x - x^2/2 - x^3/3 + x^5/5 + x^6/6 - x^7/7
For Integral_{x=0..1} set x=1
n=1 1 - 1/2 = 1/2, a(1) = 1
n=2 1 - 1/2 - 1/3 + 1/4 = 5/12, a(2) = 5
n=3 1 - 1/2 - 1/3 + 1/5 + 1/6 - 1/7 = 41/105, a(3) = 41
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..69
• StackExchange - Mathematica, No response to an infinite limit

Crossrefs

Cf. A258230, A258191, A258192, A258232.

Programs

Mathematica

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