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Triangle read by rows: T(n,k) is the number of independent sets of size k over all simple labeled graphs on n nodes, n>=0, 0<=k<=n.
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%I #19 Oct 07 2016 07:57:24

%S 1,1,1,2,4,1,8,24,12,1,64,256,192,32,1,1024,5120,5120,1280,80,1,32768,

%T 196608,245760,81920,7680,192,1,2097152,14680064,22020096,9175040,

%U 1146880,43008,448,1,268435456,2147483648,3758096384,1879048192,293601280,14680064,229376,1024,1

%N Triangle read by rows: T(n,k) is the number of independent sets of size k over all simple labeled graphs on n nodes, n>=0, 0<=k<=n.

%C Equivalently, T(n,k) is the number of size k cliques over all simple labeled graphs on n vertices.

%H Robert Israel, <a href="/A277219/b277219.txt">Table of n, a(n) for n = 0..3402</a> (rows 0 to 81, flattened)

%F T(n,k) = 2^binomial(n,2)*binomial(n,k)/2^binomial(k,2).

%e Triangle begins:

%e 1;

%e 1, 1;

%e 2, 4, 1;

%e 8, 24, 12, 1;

%e 64, 256, 192, 32, 1;

%e 1024, 5120, 5120, 1280, 80, 1;

%e 32768, 196608, 245760, 81920, 7680, 192, 1;

%e ...

%p seq(seq(2^(n*(n-1)/2-k*(k-1)/2)*binomial(n,k),k=0..n),n=0..10); # _Robert Israel_, Oct 06 2016

%t Table[Table[2^Binomial[n, 2] Binomial[n, k]/2^Binomial[k, 2], {k, 0, n}], {n,0, 7}] // Grid

%Y Cf. A079491 (row sums), A006125 (column k=0), A095340 (column k=1), A095351 (column k = 2).

%K nonn,tabl

%O 0,4

%A _Geoffrey Critzer_, Oct 05 2016