OFFSET
0,3
FORMULA
E.g.f. satisfies: A(x + log(1-x^2)) = x/(x + log(1-x^2)).
E.g.f.: A(x) = (1/x)*Series_Reversion(x + log(1-x^2)).
a(n) = A213640(n+1)/(n+1).
EXAMPLE
E.g.f.: A(x) = 1 + x + 4*x^2/2! + 33*x^3/3! + 408*x^4/4! + 6760*x^5/5! +...
Related expansions:
A(x)^2 = 1 + 2*x + 10*x^2/2! + 90*x^3/3! + 1176*x^4/4! + 20240*x^5/5! +...
-log(1 - x^2*A(x)^2)/x = x + 4*x^2/2! + 33*x^3/3! + 408*x^4/4! +...
A(x + log(1-x^2)) = 1 + x + 2*x^2/2! + 9*x^3/3! + 48*x^4/4! + 340*x^5/5! +...
PROG
(PARI) {a(n)=n!*polcoeff((1/x)*serreverse(x+log(1-x^2 +x^2*O(x^n))), n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 17 2012
STATUS
approved