A055130 Triangle T(n,k) of numbers of k-covers of an unlabeled n-set, k=1..2^n-1.

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, 1, 1, 10, 72, 417, 1973, 7745, 25830, 74017, 183420, 395311, 744495, 1229807, 1787135, 2289925, 2591162, 2591163, 2289929, 1787148, 1229846, 744592, 395498

Offset: 1

Author

Vladeta Jovovic, Jun 14 2000

Keywords

• nonn
• tabf

Examples

			Triangle begins:
[1] 1;
[2] 1, 2,  1;
[3] 1, 4,  9, 10,   6,   3,   1;
[4] 1, 7, 29, 87, 181, 287, 364, 365, 290, 187, 97, 39, 13, 4, 1;
  ...
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}}.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..2036 (rows 1..10)

Crossrefs

Row sums give A055621.

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

Cf. A052265, A368186.

Programs

PARI

\\ G(n,m) defined in A368186.
row(n)={my(m=2^n-1); Vec(G(n,m) - G(n-1,m))} \\ Andrew Howroyd, Jan 03 2024

Formula

T(n,n) = A368186(n). - Andrew Howroyd, Jan 03 2024