OFFSET
0,3
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 63*x^5 + 329*x^6 +...
By definition:
log(A(x)) = x*A(x) + x^2*A(2*x)*A(x^2)/2 + x^3*A(3*x)*A(x^3)/3 + x^4*A(4*x)*A(2*x^2)*A(x^4)/4 + x^5*A(5*x)*A(x^5)/5 + x^6*A(6*x)*A(3*x^2)*A(2*x^3)*A(x^6)/6 +...
Explicitly,
log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 43*x^4/4 + 221*x^5/5 + 1506*x^6/6 + 13196*x^7/7 + 153979*x^8/8 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n+1, x^m/m*exp(sumdiv(m, d, log(subst(A, x, m*x^d/d +x*O(x^n)))))))); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 27 2012
STATUS
approved