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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.

%I A289537 #19 Jul 16 2017 02:46:52
%S A289537 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,
%T A289537 32,0,1,126,2604,11160,10416,2016,64,0,1,254,10668,94488,188976,85344,
%U A289537 8128,128,0,1,510,43180,777240,3212592,3108960,690880,32640,256,0
%N 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.
%F A289537 T(n,k) = 2^k * A022166(n-1,k).
%e A289537 Triangle begins:
%e A289537   1;
%e A289537   1,    0;
%e A289537   1,    2,    0;
%e A289537   1,    6,    4,    0;
%e A289537   1,   14,   28,    8,    0;
%e A289537   1,   30,  140,  120,   16,    0;
%e A289537   1,   62,  620, 1240,  496,   32,    0;
%t A289537 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
%Y A289537 Cf. A022166, A182176, A289538, A289539, A289541, A289542.
%K A289537 nonn,tabl
%O A289537 0,5
%A A289537 _Geoffrey Critzer_, Jul 07 2017