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A289537
Triangle read by rows: T(n,k) is the number of k-dimensional subspaces of an n-dimensional vector space over F_2 that do not contain a given nonzero vector, n>=0, 0<=k<=n.
4
1, 1, 0, 1, 2, 0, 1, 6, 4, 0, 1, 14, 28, 8, 0, 1, 30, 140, 120, 16, 0, 1, 62, 620, 1240, 496, 32, 0, 1, 126, 2604, 11160, 10416, 2016, 64, 0, 1, 254, 10668, 94488, 188976, 85344, 8128, 128, 0, 1, 510, 43180, 777240, 3212592, 3108960, 690880, 32640, 256, 0
OFFSET
0,5
FORMULA
T(n,k) = 2^k * A022166(n-1,k).
EXAMPLE
Triangle begins:
1;
1, 0;
1, 2, 0;
1, 6, 4, 0;
1, 14, 28, 8, 0;
1, 30, 140, 120, 16, 0;
1, 62, 620, 1240, 496, 32, 0;
MATHEMATICA
Table[Table[Product[q^n - q^i, {i, 1, k}]/Product[q^k - q^i, {i, 0, k - 1}] /. q -> 2, {k, 0, n}], {n, 0, 9}] // Grid
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Jul 07 2017
STATUS
approved