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A092477 Triangle read by rows: T(n,k) = (2^k - 1)^n, 1<=k<=n.

%I A092477 #14 Jun 23 2024 11:51:51
%S A092477 1,1,9,1,27,343,1,81,2401,50625,1,243,16807,759375,28629151,1,729,
%T A092477 117649,11390625,887503681,62523502209,1,2187,823543,170859375,
%U A092477 27512614111,3938980639167,532875860165503,1,6561,5764801,2562890625,852891037441,248155780267521,67675234241018881,17878103347812890625
%N A092477 Triangle read by rows: T(n,k) = (2^k - 1)^n, 1<=k<=n.
%C A092477 T(n,1)=1; T(n,2)=A000244(n); T(n,n-1)=A086206(n); T(n,n)=A055601(n).
%C A092477 T(n,k) is the number of n X k binary matrices with no 0 rows. The triangular array becomes a rectangular array by lifting the restriction on k. [From _Geoffrey Critzer_, Dec 03 2009]
%C A092477 From _Manfred Boergens_, Jun 23 2024: (Start)
%C A092477 T(n,k) is the number of coverings of [n] by tuples (A_1,...,A_k) in P([n])^k, with P(.) denoting the power set.
%C A092477 For nonempty A_j see A218695.
%C A092477 For disjoint A_j see A089072.
%C A092477 For nonempty and disjoint A_j see A019538.
%C A092477 Lifting the restriction on k and swapping n,k gives A329943. (End)
%e A092477 Triangle begins
%e A092477  1
%e A092477  1,9;
%e A092477  1,27,343;
%e A092477  1,81,2401,50625;
%e A092477  1,243,16807,759375, 28629151 [_Geoffrey Critzer_, Dec 03 2009]
%p A092477 A092477 := proc(n,k)
%p A092477     (2^k-1)^n ;
%p A092477 end proc:
%p A092477 seq(seq( A092477(n,k),k=1..n),n=1..12) ; # _R. J. Mathar_, Nov 18 2023
%t A092477 Table[Table[(2^k - 1)^n, {k, 1, n}], {n, 1, 6}] // Grid (* _Geoffrey Critzer_, Dec 03 2009 *)
%Y A092477 Cf. A019538, A089072, A218695, A329943.
%K A092477 nonn,tabl
%O A092477 1,3
%A A092477 _Reinhard Zumkeller_, Mar 26 2004
%E A092477 More terms from _Michel Marcus_, Jun 23 2024