OFFSET
0,2
FORMULA
G.f.: A(x) = Sum_{n>=0} log( Catalan(2^n*x) )^n / n! where Catalan(x) = 2/(1+sqrt(1-4*x)).
EXAMPLE
G.f.: A(x) = 1 + 2*x + 14*x^2 + 208*x^3 + 7084*x^4 + 648128*x^5 +...
A(x) = Sum_{n>=0} log(1 +1*2^n*x +2*4^n*x^2 +5*8^n*x^3 +14*16^n*x^4 +...)^n/n!.
PROG
(PARI) a(n)=binomial(2^n + 2*n, n)*2^n/(2^n + 2*n)
(PARI) a(n)=polcoeff((2/(1+sqrt(1-4*x +x*O(x^n))))^(2^n), n)
(PARI) a(n)=polcoeff(sum(k=0, n, log( 2/(1+sqrt(1-4*2^k*x +x*O(x^n))))^k/k!), n)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 05 2008
STATUS
approved