A013926 - OEIS

A013926

a(n) = (2*n)! * D_{2*n}, where D_{2*n} = (1/Pi) * Integral_{x=0..oo} [1 - x^(2*n) / Product_{j=1..n} (x^2+j^2)] dx.

%I #8 Aug 30 2018 08:20:46

%S 1,28,1434,118960,14611150,2494744728,565526968692,164368956804288,

%T 59603021615454678,26379919529434077640,13996517446366589638636,

%U 8769645281519454489332448,6406629794568469259015608204

%N a(n) = (2*n)! * D_{2*n}, where D_{2*n} = (1/Pi) * Integral_{x=0..oo} [1 - x^(2*n) / Product_{j=1..n} (x^2+j^2)] dx.

%F a(n) = n * Sum_{k=0..n-1} T(n, k) where T(n, 0) = n^(2*n) and for k > 0, T(n, k) = (-1) ^ k * (2 / k) * binomial(2*n-1, k-1) * (n-k)^(2*n+1). - _Sean A. Irvine_, Aug 30 2018

%K nonn

%O 1,2

%A Micha Hofri (hofri(AT)cs.rice.edu)