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E.g.f. equals the imaginary part of the series F(x) = 1 + x*F(x)^i where i=sqrt(-1).
2

%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