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A323816 Number of set-systems covering n vertices with no singletons. 3
1, 0, 1, 12, 1993, 67098768, 144115187673233113, 1329227995784915871895000745158568460, 226156424291633194186662080095093570015284114833799899660370362545578585265 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..8.

FORMULA

Inverse binomial transform of A016031 shifted once to the left.

EXAMPLE

The a(3) = 12 set-systems:

  {{1,2,3}}

  {{1,2},{1,3}}

  {{1,2},{2,3}}

  {{1,3},{2,3}}

  {{1,2},{1,2,3}}

  {{1,3},{1,2,3}}

  {{2,3},{1,2,3}}

  {{1,2},{1,3},{2,3}}

  {{1,2},{1,3},{1,2,3}}

  {{1,2},{2,3},{1,2,3}}

  {{1,3},{2,3},{1,2,3}}

  {{1,2},{1,3},{2,3},{1,2,3}}

MAPLE

a:= n-> add(2^(2^(n-j)-n+j-1)*binomial(n, j)*(-1)^j, j=0..n):

seq(a(n), n=0..8);  # Alois P. Heinz, Jan 30 2019

MATHEMATICA

Table[Sum[(-1)^(n-k)*Binomial[n, k]*2^(2^k-k-1), {k, 0, n}], {n, 0, 8}]

CROSSREFS

Cf. A000295, A000371, A000612, A003465 (with singletons), A006129 (covers by pairs), A016031, A055154, A055621, A305001, A317795 (unlabeled case), A323817 (connected case).

Sequence in context: A011920 A323817 A263584 * A208252 A204622 A004823

Adjacent sequences:  A323813 A323814 A323815 * A323817 A323818 A323819

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 30 2019

STATUS

approved

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Last modified February 27 10:25 EST 2021. Contains 341649 sequences. (Running on oeis4.)