%I #4 Dec 24 2015 18:37:19
%S 0,0,2,-3,-56,720,360,-175770,2811520,27714960,-2332820800,
%T 36227931300,1242856742400,-79410400212000,881326533651200,
%U 97641790837227000,-5371510570250240000,7482518858066928000,12885336165384393984000
%N E.g.f. equals the imaginary part of the series F(x) = 1 + x*F(x)^i where i=sqrt(-1).
%F a(n) = imaginary part of C(i*n,n)/(i*n-n+1).
%e E.g.f.: 2*x^2/2! - 3*x^3/3! - 56*x^4/4! + 720*x^5/5! + 360*x^6/6! + ...
%e E.g.f. equals the imaginary part of F(x) = 1 + x*F(x)^i where
%e F(x) = 1 + x + i*x^2 - (3 + i)*x^3/2 + (6 - 7*i)*x^4/3 + (35 + 72*i)*x^5/12 - (31 - i)*x^6/2 + (1043 - 2511*i)*x^7/72 + (4074 + 4393*i)*x^8/63 - (52299 - 17108*i)*x^9/224 + (171324 - 1458013*i)*x^10/2268 + (53576369 + 32934483*i)*x^11/36288 - (1811381 - 1198743*i)*x^12/462 + ...
%o (PARI) {a(n)=n!*imag(binomial(I*n,n)/((I-1)*n+1))}
%Y Cf. A179281 (real part).
%K sign
%O 0,3
%A _Paul D. Hanna_, Jul 08 2010