OFFSET
0,1
FORMULA
The inverse zero-based binomial transform of a sequence (q(0), q(1), ..., q(m)) is the sequence p given by:
p(j) = sum_{k=0..j} (-1)^(j-k) binomial(j,k) q(k)
MATHEMATICA
q=Select[Range[100], CompositeQ];
t=Table[Sum[(-1)^(j-k)*Binomial[j, k]*q[[1+k]], {k, 0, j}], {j, 0, Length[q]-1}]
CROSSREFS
The version for prime instead of composite is A007442.
For noncomposite numbers we have A030016.
This is the first column (n=1) of A377033.
For prime-power instead of composite we have A377054.
Other arrays of differences: A095195 (prime), A376682 (noncomposite), A377033 (composite), A377038 (squarefree), A377046 (nonsquarefree), A377051 (prime-power).
KEYWORD
sign,new
AUTHOR
Gus Wiseman, Oct 18 2024
STATUS
approved