expectedSyzygies -- compute the expected Betti numbers of an artinian module

Compute the expected Betti numbers of an graded artinian module with smallest degree generator in degree 0 from its Hilbert function over a standard graded polynomial ring in n variables. The answer is a reasonable guess, if there are precisely n sign changes in the Hilbert numerator

(1-t)ⁿ ∑ _i≥0 H_i tⁱ= ∑_i=0ⁿ ∑_j  β_ij t^j

i1 : expectedSyzygies(5,{1,5,8})

            0 1  2  3  4 5
o1 = total: 1 7 35 56 35 8
         0: 1 .  .  .  . .
         1: . 7  .  .  . .
         2: . . 35 56 35 8

o1 : BettiTally