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.

1, 1, 4, -9, -20, 55, 210, -1085, -7000, 53235, 462350, -4500265, -48454980, 571411295, 7321388410, -101249656725, -1502852293040, 23827244817355, 401839065437670, -7182224591785985, -135607710526966300, 2696935204638786615, 56349204870460046930, -1234002202313888987245

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..24.

Formula

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

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

Mathematica

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

Crossrefs

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

Cf. A003422

Sequence in context: A331942 A111587 A161221 * A225986 A147971 A197869

Adjacent sequences: A130042 A130043 A130044 * A130046 A130047 A130048

Keyword

frac,sign

Author

Wouter Meeussen, May 02 2007

Status

approved