OFFSET
1,2
FORMULA
Forms the logarithmic derivative of A205476.
EXAMPLE
L.g.f.: L(x) = x + 3*x^2/2 + 4*x^3/3 + 7*x^4/4 + 11*x^5/5 + 12*x^6/6 +...
By definition:
L(x) = x*(1+x) + x^2*(1+2*x)*(1+x^2)/2 + x^3*(1+3*x)*(1+x^3)/3 + x^4*(1+4*x)*(1+2*x^2)*(1+x^4)/4 + x^5*(1+5*x)*(1+x^5)/5 + x^6*(1+6*x)*(1+3*x^2)*(1+2*x^3)*(1+x^6)/6 +...
Exponentiation yields the g.f. of A205476:
exp(L(x)) = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 8*x^5 + 12*x^6 + 20*x^7 +...
MATHEMATICA
max = 50; s = Sum[(x^(n-1)/n)*Product[1+n*x^d/d, {d, Divisors[n]}], {n, 1, max}] + O[x]^max; CoefficientList[s, x]*Range[max] (* Jean-François Alcover, Dec 23 2015 *)
PROG
(PARI) {a(n)=n*polcoeff(sum(m=1, n+1, x^m/m*exp(sumdiv(m, d, log(1+m*x^d/d+x*O(x^n))))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 27 2012
STATUS
approved