A196869 G.f. A(x) satisfies: A(x)^3 + A(-x)^3 = 2 and A(x)^2 - A(-x)^2 = 24*x.

1, 6, -36, 216, -2592, 23328, -311040, 3265920, -45349632, 517321728, -7336562688, 88159684608, -1266403590144, 15771513618432, -228509902503936, 2921050338066432, -42583086769766400, 555279063084564480, -8132204141176946688, 107718176292801085440

Offset: 0

Author

Paul D. Hanna, Oct 06 2011

Keywords

• sign

Examples

			G.f.: A(x) = 1 + 6*x - 36*x^2 + 216*x^3 - 2592*x^4 + 23328*x^5 +...
where
A(x)^2 = 1 + 12*x - 36*x^2 - 1296*x^4 - 108864*x^6 - 12317184*x^8 +...
A(x)^3 = 1 + 18*x - 432*x^3 - 23328*x^5 - 2239488*x^7 - 272097792*x^9 +...
		

Crossrefs

Cf. A196868, A193618, A193619, A196864, A196865, A196866, A196867.

Programs

PARI

{a(n)=local(A=[1,6]);for(k=2,n,A=concat(A,0);if(k%2==1,A[#A]=-Vec(Ser(A)^2)[#A]/2,A[#A]=-Vec(Ser(A)^3)[#A]/3));A[n+1]}