A316912 - OEIS

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).

%I #7 Aug 11 2018 00:38:03

%S 1,6,40,288,10560,24024,792064,34728960,3627008,302356454400,

%T 307660953600,98050867200,15038824120320,4757532010463232,

%U 577952036826644480,26189033224273920,358597702262241361920,244498433360619110400,143982410756809031680

%N 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).

%t 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}]

%t Denominator[FracData[5000]]

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

%K nonn,frac

%O 0,2

%A _Bradley Klee_, Jul 16 2018