OFFSET
0,3
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 21*x^3 + 283*x^4 + 6501*x^5 + 234363*x^6 +...
where, by definition,
A(x) = 1 + 1*x/(1+x) + 1*4*x^2/((1+x)*(1+4*x)) + 1*4*10*x^3/((1+x)*(1+4*x)*(1+10*x)) + 1*4*10*20*x^4/((1+x)*(1+4*x)*(1+10*x)*(1+20*x)) + 1*4*10*20*35*x^5/((1+x)*(1+4*x)*(1+10*x)*(1+20*x)*(1+35*x)) + 1*4*10*20*35*56*x^6/((1+x)*(1+4*x)*(1+10*x)*(1+20*x)*(1+35*x)*(1+56*x)) +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, 1, A=sum(m=0, n, prod(k=1, m, 1-1/(1+k*(k+1)*(k+2)/3!*x +x*O(x^n))))); polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 06 2013
STATUS
approved