A094601 G.f. satisfies: A(x) = F(x*A(x)), where F(x) is the g.f. of A094600.

1, 1, 3, 12, 50, 234, 1125, 5620, 28753, 150106, 796240, 4279232, 23251672, 127518750, 704957715, 3924307492, 21978740682, 123758612644, 700204091361, 3978636187708, 22694470914700, 129904466979030, 745949776425002

Offset: 0

Author

Paul D. Hanna, May 13 2004

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 50*x^4 + 234*x^5 + 1125*x^6 + 5620*x^7 +...
where
A(x) = Sum_{n>=1} A094600(2*n)*x^n/(n+1), and
log(A(x)) = Sum_{n>=1} A094600(2*n-1)*x^n/n,
log(A(x)) = x + 5*x^2/2 + 28*x^3/3 + 145*x^4/4 + 831*x^5/5 + 4664*x^6/6 +...
		

Crossrefs

Cf. A094600, A094558.

Programs

PARI

{a(n)=local(A=1+x); for(i=1,n, A=subst(A+x*A', x, x^2*A^2)+x*A*subst(A', x, x^2*A^2)/subst(A, x, x^2*A^2) +x*O(x^n)); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Formula

a(n) = A094600(2*n)/(n+1) for n>=0.

G.f.: A(x) = exp( Sum_{n>=1} A094600(2*n-1)*x^n/n ).

G.f. satisfies: A(x) = A(y) + x*A(x)*A'(y)/A(y) + x^2*A(x)^2*A'(y) where y = x^2*A(x)^2.

Extensions

Entry revised by Paul D. Hanna, Apr 17 2013