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A306021 Number of set-systems spanning {1,...,n} in which all sets have the same size. 41

%I

%S 1,1,2,6,54,1754,1102746,68715913086,1180735735356265746734,

%T 170141183460507906731293351306656207090,

%U 7237005577335553223087828975127304177495735363998991435497132232365910414322

%N Number of set-systems spanning {1,...,n} in which all sets have the same size.

%F a(n) = Sum_{k = 0...n} (-1)^(n - k) binomial(n, k) (1 - k + Sum_{d = 1...k} 2^binomial(k, d)).

%e The a(3) = 6 set-systems in which all sets have the same size:

%e {{1,2,3}}

%e {{1},{2},{3}}

%e {{1,2},{1,3}}

%e {{1,2},{2,3}}

%e {{1,3},{2,3}}

%e {{1,2},{1,3},{2,3}}

%t Table[Sum[(-1)^(n-k)*Binomial[n,k]*(1+Sum[2^Binomial[k,d]-1,{d,k}]),{k,0,n}],{n,12}]

%Y Cf. A000005, A001315, A007716, A038041, A049311, A283877, A298422, A306017, A306018, A306019, A306020.

%K nonn

%O 0,3

%A _Gus Wiseman_, Jun 17 2018

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Last modified April 11 06:11 EDT 2021. Contains 342886 sequences. (Running on oeis4.)