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

0,3

Links

Table of n, a(n) for n=0..22.

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.

Example

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 +...

Prog

(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), ", "))

Crossrefs

Cf. A094600, A094558.

Sequence in context: A151180 A268650 A151181 * A242155 A009024 A265083

Adjacent sequences: A094598 A094599 A094600 * A094602 A094603 A094604

Keyword

nonn

Author

Paul D. Hanna, May 13 2004

Extensions

Entry revised by Paul D. Hanna, Apr 17 2013

Status

approved