OFFSET
1,2
COMMENTS
Sum[ -(-1)^(k) n/k(n-1)/(k+1), {k,1,n}] can be simplified to -((-1+n)*n*(1+(2*(-1)^n)/n +(-2+(-1)^n)*Log[2]- ((-1)^n*(-3*PolyGamma[0,n/2]+ 2*PolyGamma[0,n]+ PolyGamma[0,(3+n)/2]))/2))
LINKS
FORMULA
G.f.: -(4*x^6-6*x^4-6*x^3+2*x^2+4*x+1)/(-2*x^3+2*x^2+x-1)
For n>4, a(n) = (4 - n%2) * 2^floor((n-1)/2) + 1. - Ralf Stephan, Mar 17 2004
MATHEMATICA
Position[Table[Sum[ -(-1)^(k) n/k(n-1)/(k+1), {k, 1, n}] (n!!), {n, 1, 1025}], _Integer]// Flatten or, equivalently, CoefficientList[Series[ -(4x^6-6*x^4-6*x^3+2*x^2+4*x+1)/(-2*x^3+2*x^2+x-1), {x, 0, 48}], x]
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Wouter Meeussen, Dec 11 2002
STATUS
approved