The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #14 Nov 30 2014 04:13:06
%S 1,1,0,-6,-12,20,300,252,-3024,-36720,106560,110880,12212640,
%T -125629920,1005286464,-16865735040,252900345600,-3575747185920,
%U 58447092395520,-1014901444454400,18218754479923200,-346655486035998720,6952232946445839360,-145913061049673702400,3205301440394904238080
%N Exponential generating function = (1+x)^(1-x^2).
%F a(n) ~ 2 * (-1)^n * n! / n^2 * (1 + 4*log(n)/n). - _Vaclav Kotesovec_, Nov 30 2014
%e (1+x)^(1-x^2) = 1 + x - x^3 - 1/2*x^4 + 1/6*x^5 + 5/12*x^6 + 1/20*x^7 - 3/40*x^8 - 17/168*x^9 + 37/1260*x^10 + 1/360*x^11 + 257/10080*x^12 - ...
%t CoefficientList[Series[(1+x)^(1-x^2), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Nov 30 2014 *)
%o (PARI) Vec(serlaplace((1+x+O(x^25))^(1-x^2)))
%Y Cf. A005727, A007120, A247212.
%K sign
%O 0,4
%A _Franklin T. Adams-Watters_, Nov 29 2014