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Triangle T(n,k) of numbers of k-covers of an unlabeled n-set, k=1..2^n-1.
3

%I #14 Jan 03 2024 15:09:23

%S 1,1,2,1,1,4,9,10,6,3,1,1,7,29,87,181,287,364,365,290,187,97,39,13,4,

%T 1,1,10,72,417,1973,7745,25830,74017,183420,395311,744495,1229807,

%U 1787135,2289925,2591162,2591163,2289929,1787148,1229846,744592,395498

%N Triangle T(n,k) of numbers of k-covers of an unlabeled n-set, k=1..2^n-1.

%H Andrew Howroyd, <a href="/A055130/b055130.txt">Table of n, a(n) for n = 1..2036</a> (rows 1..10)

%F T(n,n) = A368186(n). - _Andrew Howroyd_, Jan 03 2024

%e Triangle begins:

%e [1] 1;

%e [2] 1, 2, 1;

%e [3] 1, 4, 9, 10, 6, 3, 1;

%e [4] 1, 7, 29, 87, 181, 287, 364, 365, 290, 187, 97, 39, 13, 4, 1;

%e ...

%e There are 9 3-covers of an unlabeled 3-set: {{1,2},{2,3},{1,2,3}}, {{1,2},{2,3},{1,3}}, {{1,2},{3},{1,2,3}}, {{1},{1,2},{1,2,3}}, {{1,2},{2,3},{3}}, {{1,2},{2},{2,3}}, {{1},{2},{1,2,3}}, {{1},{2},{1,3}} and {{1},{2},{3}}.

%o (PARI) \\ G(n,m) defined in A368186.

%o row(n)={my(m=2^n-1); Vec(G(n,m) - G(n-1,m))} \\ _Andrew Howroyd_, Jan 03 2024

%Y Row sums give A055621.

%Y Columns k=1..3 are A000012, A014616(n-1), A055195.

%Y Cf. A052265, A368186.

%K nonn,tabf

%O 1,3

%A _Vladeta Jovovic_, Jun 14 2000