OFFSET
1,1
FORMULA
For all n > 0 we have: 2 = Sum_{d|n} binomial(-a(d) + n/d - 1, n/d).
EXAMPLE
2x/(1-x) = (1-x)^(-2) - 1 + (1-x^2)^1 - 1 + (1-x^3)^2 - 1 + (1-x^4)^3 - 1 + ...
MAPLE
a:= n-> add(binomial(n/d-1-a(d), n/d), d=
numtheory[divisors](n) minus {n})-2:
seq(a(n), n=1..60); # Alois P. Heinz, Aug 27 2017
MATHEMATICA
nn=60;
rus=SolveAlways[Normal[Series[2x/(1-x)==Sum[(1-x^n)^a[n]-1, {n, nn}], {x, 0, nn}]], x];
Array[a, nn]/.First[rus]
CROSSREFS
KEYWORD
sign
AUTHOR
Gus Wiseman, Aug 16 2017
STATUS
approved