A094601 - OEIS

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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

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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