OFFSET
1,2
FORMULA
a(n) = n * Sum_{k=0..[n/2]} C(n-k,k)*sigma(n-k)^k/(n-k) for n>=1.
EXAMPLE
L.g.f.: L(x) = x + 3*x^2/2 + 10*x^3/3 + 35*x^4/4 + 116*x^5/5 +...
L(x) = (1+x)*x + (1+3*x)^2*x^2/2 + (1+4*x)^3*x^3/3 + (1+7*x)^4*x^4/4 +...
exp(L(x)) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 40*x^5 + 154*x^6 +... (A159308).
PROG
(PARI) {a(n)=n*polcoeff(sum(m=1, n+1, (1+sigma(m)*x+x*O(x^n))^m*x^m/m), n)}
(PARI) {a(n)=n*sum(k=0, n\2, binomial(n-k, k)*sigma(n-k)^k/(n-k))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 10 2009
STATUS
approved