A210525 G.f.: A(x) = Sum_{n>=0} x^n * A(n*x) * A(-n*x).

1, 1, 1, 2, 5, 17, 129, 823, 16549, 203762, 9057969, 229117047, 20251050469, 1099941609906, 182745344595201, 21826976698036317, 6625997170286326085, 1760792727174811634066, 963263479575497024110193, 572732462137043288595101258, 560867188756075075604736149189

Offset: 0

Author

Paul D. Hanna, Jan 27 2013

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 17*x^5 + 129*x^6 + 823*x^7 +...
such that
A(x) = 1 + x*A(x)*A(-x) + x^2*A(2*x)*A(-2*x) + x^3*A(3*x)*A(-3*x) + x^4*A(4*x)*A(-4*x) + x^5*A(5*x)*A(-5*x) +...
where
A(x)*A(-x) = 1 + x^2 + 7*x^4 + 230*x^6 + 31667*x^8 + 17739221*x^10 + 40061321883*x^12 + 363330478847435*x^14 +...
		

Crossrefs

Cf. A125282, A196196.

Programs

PARI

{a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=sum(k=0, n, x^k*subst(A,x,k*x +x*O(x^n))*subst(A,x,-k*x +x*O(x^n)))  );polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))