OFFSET
0,3
FORMULA
Logarithmic derivative yields A184513.
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 9*x^3 + 33*x^4 + 115*x^5 + 445*x^6 +...
The log of the g.f. equals the series:
log(A(x)) = x/sqrt(1-4*x) + (x^2/2)/sqrt(1-8*x^2) + (x^3/3)/sqrt(1-16*x^3) + (x^4/4)/sqrt(1-32*x^4) + (x^5/5)/sqrt(1-64*x^5) +...
and may be expressed in terms of the central binomial coefficients (A000984).
Explicitly, the logarithm begins:
log(A(x)) = x + 5*x^2/2 + 19*x^3/3 + 89*x^4/4 + 351*x^5/5 + 1601*x^6/6 +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, (x^m/m)/sqrt(1-2*(2*x)^m+x*O(x^n)))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 18 2011
STATUS
approved