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A323816 Number of set-systems covering n vertices with no singletons. 7
1, 0, 1, 12, 1993, 67098768, 144115187673233113, 1329227995784915871895000745158568460, 226156424291633194186662080095093570015284114833799899660370362545578585265 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
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}]
PROG
(Magma)
[(&+[(-1)^(n-j)*Binomial(n, j)*2^(2^j -j-1): j in [0..n]]): n in [0..12]]; // G. C. Greubel, Oct 05 2022
(SageMath)
def A323816(n): return sum((-1)^j*binomial(n, j)*2^(2^(n-j) -n+j-1) for j in range(n+1))
[A323816(n) for n in range(12)] # G. C. Greubel, Oct 05 2022
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 A369336
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 30 2019
STATUS
approved

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Last modified April 23 06:04 EDT 2024. Contains 371906 sequences. (Running on oeis4.)