OFFSET
0,3
COMMENTS
Compare g.f. to the o.g.f. of Bell numbers (A000110): Sum_{n>=0} x^n/Product_{k=1..n} (1-k*x).
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 13*x^4 + 37*x^5 + 114*x^6 + 384*x^7 +...
By definition:
A(x) = 1 + x/(1-x) + x^2/((1-x)*(1-2*x)) + x^3/((1-x)*(1-3*x)) + x^4/((1-x)*(1-2*x)*(1-4*x)) + x^5/((1-x)*(1-5*x)) + x^6/((1-x)*(1-2*x)*(1-3*x)*(1-6*x)) +...
PROG
(PARI) {a(n)=polcoeff(1+sum(m=1, n, x^m*exp(-sumdiv(m, d, log(1-d*x +x*O(x^n))))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 28 2012
STATUS
approved