A130045 - OEIS

A130045

Denominator of polynomial a[1]=1, a[2]->1+1/(x*a[1]), a[3]->1+1/(2*x*a[2]), a[4]->1+1/(3*x*a[3]),.. giving 1,(1+x)/x,(3+2*x)/(2*(1+x)),(2+11*x+6*x^2)/(3*x*(3+2*x)), .. at x-> -1. Absolute values are equal to A067078(n)/n.

%I #7 Mar 30 2012 18:53:56

%S 1,1,4,-9,-20,55,210,-1085,-7000,53235,462350,-4500265,-48454980,

%T 571411295,7321388410,-101249656725,-1502852293040,23827244817355,

%U 401839065437670,-7182224591785985,-135607710526966300,2696935204638786615,56349204870460046930,-1234002202313888987245

%N Denominator of polynomial a[1]=1, a[2]->1+1/(x*a[1]), a[3]->1+1/(2*x*a[2]), a[4]->1+1/(3*x*a[3]),.. giving 1,(1+x)/x,(3+2*x)/(2*(1+x)),(2+11*x+6*x^2)/(3*x*(3+2*x)), .. at x-> -1. Absolute values are equal to A067078(n)/n.

%C The iterated form (see Mathematica line) links some seemingly disparate sequences.

%F A067078 has recurrence a(1) = 1, a(2) = 2, a(n) = (n-1)*a(n-1) - (n-2)*a(n-2).

%F abs(a(n))=(n-1)*sum(k!,k=0..n-3)+(n-1), n>1. [From _Gary Detlefs_, Feb 05 2011]

%t Denominator[Together[k=1;NestList[1+1/((k++)x #)&,x,24]]]/.x->(-1)

%Y Cf. A067078, A052169, A002467, A001053, A093858.

%Y Cf. A003422

%K frac,sign

%O 1,3

%A _Wouter Meeussen_, May 02 2007