OFFSET
0,4
COMMENTS
Let P_n be the set of n X n idempotent matrices over GF(2) with the ordering: E<=F iff EF=E=FE. Then T(n,k) = Sum mu(0,E) where the sum is taken over the elements in P_n of rank k and mu is the Moebius mu incidence function of P_n.
To obtain the inverse, we regard the triangle as a lower triangular matrix, but then ignore the part above the diagonal.
FORMULA
EXAMPLE
Triangle begins
1;
-1, 1;
5, -6, 1;
-113, 140, -28, 1;
10879, -13560, 2800, -120, 1;
-4324129, 5395984, -1120960, 49600, -496, 1;
...
MATHEMATICA
nn = 6; B[n_] = Product[q^n - q^i, {i, 0, n - 1}] /. q -> 2; e[x_] := Sum[x^n/B[n], {n, 0, nn}]; Table[B[n], {n, 0, nn}]*CoefficientList[Series[ e[y x]/e[x], {x, 0, nn}], {x, y}] // Grid
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Geoffrey Critzer, Jun 03 2024
STATUS
approved