OFFSET
0,3
COMMENTS
Compare to the identity:
Sum_{n>=0} x^n * Product_{k=1..n} (1 + k*x)/(1 + x + k*x^2) = 1/(1-x).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..300
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 9*x^3 + 29*x^4 + 99*x^5 + 355*x^6 + 1333*x^7 +...
where
A(x) = 1 + x*(1+x)/(1-x-x^2) + x^2*(1+x)*(1+2*x)/((1-x-x^2)*(1-x-2*x^2)) + x^3*(1+x)*(1+2*x)*(1+3*x)/((1-x-x^2)*(1-x-2*x^2)*(1-x-3*x^2)) + x^4*(1+x)*(1+2*x)*(1+3*x)*(1+4*x)/((1-x-x^2)*(1-x-2*x^2)*(1-x-3*x^2)*(1-x-4*x^2)) +...
PROG
(PARI) {a(n)=polcoeff( sum(m=0, n, x^m*prod(k=1, m, (1+k*x)/(1-x-k*x^2 +x*O(x^n))) ), n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 06 2013
STATUS
approved