OFFSET
0,3
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 19*x^4 + 114*x^5 + 1213*x^6 +...
where
log(A(x)) = (1 + x*A(x))*x + (1 + 2^2*x*A(x) + x^2*A(x)^2)*x^2/2 +
(1 + 3^3*x*A(x) + 3^3*x^2*A(x)^2 + x^3*A(x)^3)*x^3/3 +
(1 + 4^4*x*A(x) + 6^4*x^2*A(x)^2 + 4^4*x^3*A(x)^3 + x^4*A(x)^4)*x^4/4 +
(1 + 5^5*x*A(x) + 10^5*x^2*A(x)^2 + 10^5*x^3*A(x)^3 + 5^5*x^4*A(x)^4 + x^5*A(x)^5)*x^5/5 +...
more explicitly,
log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 55*x^4/4 + 461*x^5/5 + 6486*x^6/6 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(j=0, m, binomial(m, j)^m*(x*A+x*O(x^n))^j)*x^m/m))); polcoeff(A, n, x)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 31 2011
STATUS
approved