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%I #4 Dec 24 2015 18:38:02
%S 1,1,0,-9,48,350,-11160,73010,2607360,-84724380,274118400,58934005900,
%T -1878039820800,-11920073789000,2984939450438400,-86257610003799000,
%U -2337484592701440000,281472063119891306000,-6445251832278924288000
%N E.g.f. equals the real part of the series F(x) = 1 + x*F(x)^i where i=sqrt(-1).
%F a(n) = real part of C(i*n,n)/(i*n-n+1).
%e E.g.f.: 1 + x - 9*x^3/3! + 48*x^4/4! + 350*x^5/5! - 11160*x^6/6! + ...
%e E.g.f. equals the real 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!*real(binomial(I*n,n)/((I-1)*n+1))}
%Y Cf. A179281 (imaginary part).
%K sign
%O 0,4
%A _Paul D. Hanna_, Jul 08 2010
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