A171191 G.f. satisfies: A(x) = exp( Sum_{n>=1} [A(x)^n + 1/A(-x)^n]*x^n/n ).

1, 2, 7, 20, 73, 263, 1111, 4451, 20161, 85304, 401401, 1755593, 8465311, 37866818, 185756605, 844627115, 4196759383, 19321634594, 96962969047, 450810982796, 2280344734891, 10686378006479, 54406554842287, 256637809742444

Offset: 0

Author

Paul D. Hanna, Dec 05 2009

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 2*x + 7*x^2 + 20*x^3 + 73*x^4 + 263*x^5 + 1111*x^6 + ...
log(A(x)) = [A(x)+1/A(-x)]*x + [A(x)^2+1/A(-x)^2]*x^2/2 + [A(x)^3+1/A(-x)^3]*x^3/3 + ...
		

Crossrefs

Cf. A171190, A171199.

Programs

PARI

{a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=exp(sum(m=1,n,(A^m+subst(A^-m,x,-x)+x*O(x^n))*x^m/m)));polcoeff(A,n)}

PARI

{a(n)=local(A=1+x);for(i=1,n,A=(1-x*A+x*O(x^n))^-1*(1-x/subst(A,x,-x)+x*O(x^n))^-1);polcoeff(A,n)} \\ Paul D. Hanna, Dec 06 2009

Formula

G.f. satisfies: A(x) = 1/[(1 - x*A(x))*(1 - x/A(-x))]. - Paul D. Hanna, Dec 06 2009