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A143048 G.f. satisfies: A(x) = 1 + x*A(-x)^5. 4

%I

%S 1,1,-5,-15,165,630,-8151,-33780,474045,2052495,-30206330,-134392230,

%T 2040588775,9248893360,-143569282680,-659546365020,10407737293965,

%U 48303692377425,-771991701692175,-3611789245335285,58311219888996170,274581478640096340

%N G.f. satisfies: A(x) = 1 + x*A(-x)^5.

%F G.f. satisfies: A(x) = 1 + x*(1 - x*A(x)^5)^5.

%F G.f. satisfies: [A(x)^6 + A(-x)^6]/2 = [A(x)^5 + A(-x)^5]/2.

%e A(x) = 1 + x - 5*x^2 - 15*x^3 + 165*x^4 + 630*x^5 - 8151*x^6 -++-...

%e A(x)^5 = 1 + 5*x - 15*x^2 - 165*x^3 + 630*x^4 + 8151*x^5 - 33780*x^6 -...

%e A(x)^6 = 1 + 6*x - 15*x^2 - 220*x^3 + 630*x^4 + 11286*x^5 - 33780*x^6 -...

%e Note that a bisction of A^6 equals a bisection of A^5.

%o (PARI) a(n)=local(A=x+x*O(x^n));for(i=0,n,A=1+x*subst(A,x,-x)^5);polcoeff(A,n)

%Y Cf. A143045, A143046, A143047, A143049.

%K sign

%O 0,3

%A _Paul D. Hanna_, Jul 19 2008

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Last modified April 11 18:59 EDT 2021. Contains 342888 sequences. (Running on oeis4.)