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A344110 Triangle read by rows: T(n,k) = 2^(n*k), n >= 0, 0 <= k <= n.

%I A344110 #39 Jan 03 2023 06:19:10
%S A344110 1,1,2,1,4,16,1,8,64,512,1,16,256,4096,65536,1,32,1024,32768,1048576,
%T A344110 33554432,1,64,4096,262144,16777216,1073741824,68719476736,1,128,
%U A344110 16384,2097152,268435456,34359738368,4398046511104,562949953421312
%N A344110 Triangle read by rows: T(n,k) = 2^(n*k), n >= 0, 0 <= k <= n.
%C A344110 T(n, k) is the number of relations from an n-element set into a k-element set, n >= 0, 0 <= k <= n.
%C A344110 T(n,k) is the size of the right principal ideal generated by A where A is an n X n matrix over GF(2) having rank k.  The right principal ideal of A contains precisely the matrices whose image is contained in the image of A. - _Geoffrey Critzer_, Sep 25 2022
%H A344110 Michael De Vlieger, <a href="/A344110/b344110.txt">Table of n, a(n) for n = 0..1325</a> (rows n = 0..50, flattened)
%H A344110 Mohammad K. Azarian, <a href="https://doi.org/10.12988/imf.2022.912321">Remarks and Conjectures Regarding Combinatorics of Discrete Partial Functions</a>, Int'l Math. Forum (2022) Vol. 17, No. 3, 129-141.
%F A344110 T(n,k) = 2^(n*k).
%F A344110 T(n,k) = Sum_{j=0..k} A288853(n,j)*A022166(n,j). - _Geoffrey Critzer_, Jan 02 2023
%e A344110 T(3,3) = number of relations from a 3-element set into a 3-element set=2^(3*3)=512.
%e A344110 Triangle begins:
%e A344110    1
%e A344110    1   2
%e A344110    1   4      16
%e A344110    1   8      64      512
%e A344110    1  16     256     4096      65536
%e A344110    1  32    1024    32768    1048576    33554432
%e A344110    ...
%t A344110 Table[2^(n*k), {n, 0, 10}, {k, 0, n}]
%Y A344110 Cf. A000079, A089072, A008292, A031971, A117401, A344260 (row sums).
%Y A344110 Cf. A022166, A288853.
%K A344110 easy,nonn,tabl
%O A344110 0,3
%A A344110 _Mohammad K. Azarian_, May 10 2021