A007537 Number of proper covers of an n-set.

0, 1, 45, 15913, 1073579193, 4611686005542975085, 85070591730234615801280047645054636261, 28948022309329048855892746252171976961956366698726387156269151989162886489297

Offset: 1

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• nonn
• easy
• nice

Comments

This sequence is likely to occur with doubled values and offset 0:

A000371(n) - 2^(2^n-1) = 1, 0, 2, 90, 31826, 2147158386, ... - Tilman Piesk, May 24 2024

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..11
• A. J. Macula, Covers of a finite set, Math. Mag., 67 (1994), 141-144.
• Eric Weisstein's World of Mathematics, Proper Cover.

Crossrefs

Cf. A003465, A000371.

Programs

Maple

A007537 := proc(n) (1/2)*add((-1)^k*binomial(n,k)*2^(2^(n-k)),k=0..n)-2^(2^n)/4 end;

Mathematica

Table[1/2 Sum[(-1)^k Binomial[n,k]2^(2^(n-k)),{k,0,n}]-2^2^n/4,{n,8}] (* Harvey P. Dale, Oct 31 2011 *)

Formula

a(n) ~ 2^(2^n)/4. - Vaclav Kotesovec, Jul 02 2016

a(n) = A003465(n) - 2^(2^n-2). - Tilman Piesk, May 24 2024

Extensions

One more term from Emeric Deutsch, Aug 01 2005