OFFSET
0,4
COMMENTS
Compare to: exp( Sum_{n>=1} (x^n/n)/(1+x^n) ) = Sum_{n>=0} x^(n*(n+1)/2).
EXAMPLE
G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 7*x^4 + 18*x^5 + 51*x^6 + 147*x^7 +...
where
log(A(x)) = A(x)*x/(1+x) + A(x)^2*(x^2/2)/(1+x^2) + A(x)^3*(x^3/3)/(1+x^3) + A(x)^4*(x^4/4)/(1+x^4) + A(x)^5*(x^5/5)/(1+x^5) +...
explicitly,
log(A(x)) = x + x^2/2 + 7*x^3/3 + 17*x^4/4 + 56*x^5/5 + 187*x^6/6 + 617*x^7/7 + 2033*x^8/8 + 6811*x^9/9 + 22906*x^10/10 +...
PROG
(PARI) {a(n) = local(A=1+x); for(i=1, n, A = exp( sum(k=1, n, A^k*x^k/k/(1+x^k +x*O(x^n))))); polcoeff(A, n)}
for(n=0, 40, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 01 2015
STATUS
approved