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

1, 1, 9, 1, 27, 343, 1, 81, 2401, 50625, 1, 243, 16807, 759375, 28629151, 1, 729, 117649, 11390625, 887503681, 62523502209, 1, 2187, 823543, 170859375, 27512614111, 3938980639167, 532875860165503, 1, 6561, 5764801, 2562890625

Offset

1,3

Comments

T(n,1)=1; T(n,2)=A000244(n); T(n,n-1)=A086206(n); T(n,n)=A055601(n).

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]

Links

Table of n, a(n) for n=1..32.

Example

Triangle begins
 1
 1,9;
 1,27,343;
 1,81,2401,50625;
 1,243,16807,759375, 28629151 [From Geoffrey Critzer, Dec 03 2009]

Maple

A092477 := proc(n, k)
    (2^k-1)^n ;
end proc:
seq(seq( A092477(n, k), k=1..n), n=1..12) ; # R. J. Mathar, Nov 18 2023

Mathematica

Table[Table[(2^k - 1)^n, {k, 1, n}], {n, 1, 6}] // Grid [From Geoffrey Critzer, Dec 03 2009]

Crossrefs

Sequence in context: A181318 A202006 A195278 * A019433 A276634 A050312

Adjacent sequences: A092474 A092475 A092476 * A092478 A092479 A092480

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Mar 26 2004

Status

approved