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From an asymptotic expansion for Pi.
0

%I #10 Sep 27 2019 05:57:37

%S 1,1,1,-1,-5,23,53,-593,-5165,110123,231743,-8113223,-33497425,

%T 1744764499,3563384029,-258115578289,-4191097954685,402402297433523,

%U 813628574192123,-99925014024526283,-403078530716889835,61606956815080291849

%N From an asymptotic expansion for Pi.

%D R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 481.

%p v := asympt(16^n/(2*n)!^2*n!^4/n,n,24); seq(numer(op(i,v)),i=1..nops(v));

%t nmax = 20; Numerator[CoefficientList[Series[Binomial[2 n, n]^2/(2^(4 n)/Pi/n), {n, Infinity, nmax}], 1/n]]*(-1)^Range[0, nmax] (* _Vaclav Kotesovec_, Sep 27 2019 *)

%Y Cf. A002894.

%K sign

%O 0,5

%A _Simon Plouffe_