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A007537 Number of proper covers of an n-set.
(Formerly M5287)
7
0, 1, 45, 15913, 1073579193, 4611686005542975085, 85070591730234615801280047645054636261, 28948022309329048855892746252171976961956366698726387156269151989162886489297 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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.

FORMULA

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

MAPLE

A007537 := proc(n) 1/2*sum((-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 *)

CROSSREFS

Cf. A003465.

Sequence in context: A201004 A171118 A199521 * A287434 A225991 A125113

Adjacent sequences:  A007534 A007535 A007536 * A007538 A007539 A007540

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Simon Plouffe

EXTENSIONS

One more term from Emeric Deutsch, Aug 01 2005

STATUS

approved

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Last modified April 13 07:51 EDT 2021. Contains 342935 sequences. (Running on oeis4.)