A316912 Define K(n) = Integral_{t=0..1} (-1/2)^n/(1+t)*((1-t)^2*t^2/(1+t))^n*dt and write K(n) = d(n)*log(2) - b(n)/a(n) where a(n), d(n), b(n) are positive integers; sequence gives a(n).

1, 6, 40, 288, 10560, 24024, 792064, 34728960, 3627008, 302356454400, 307660953600, 98050867200, 15038824120320, 4757532010463232, 577952036826644480, 26189033224273920, 358597702262241361920, 244498433360619110400, 143982410756809031680

Offset: 0

Author

Bradley Klee, Jul 16 2018

Keywords

• nonn
• frac

Crossrefs

Integer Part: A190726. Numerators: A316911. Similar Pi Approximation: A123178, A305997, A305998.

Programs

Mathematica

FracData[n0_]:=RecurrenceTable[{2*(n-1)*(2*n-3)*(2*n-1)*(33*n-8)*a[n-2]+ 9*(2*n-1)*(693*n^3-1554*n^2+989*n-160)*a[n-1] -3*n*(3*n-2)*(3*n-1)*(33*n-41)*a[n] == 0, a[0]==0, a[1]==25/6}, a, {n, 0, n0}]
Denominator[FracData[5000]]