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A306020
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a(n) is the number of set-systems using nonempty subsets of {1,...,n} in which all sets have the same size.
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10
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1, 2, 5, 16, 95, 2110, 1114237, 68723671292, 1180735735906024030715, 170141183460507917357914971986913657850, 7237005577335553223087828975127304179197147198604070555943173844710572689401
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = 1 - n + Sum_{d = 1..n} 2^binomial(n, d).
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EXAMPLE
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a(3) = 16 set-systems in which all sets have the same size:
{}
{{1}}
{{2}}
{{3}}
{{1,2}}
{{1,3}}
{{2,3}}
{{1,2,3}}
{{1},{2}}
{{1},{3}}
{{2},{3}}
{{1,2},{1,3}}
{{1,2},{2,3}}
{{1,3},{2,3}}
{{1},{2},{3}}
{{1,2},{1,3},{2,3}}
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MAPLE
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a := n -> 1-n+add(2^binomial(n, d), d = 1 .. n):
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MATHEMATICA
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Table[1+Sum[2^Binomial[n, d]-1, {d, n}], {n, 10}]
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PROG
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(PARI) a(n) = 1 - n + sum(d = 1, n, 2^binomial(n, d)); \\ Michel Marcus, Aug 10 2023
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CROSSREFS
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Cf. A000005, A001315, A007716, A038041, A049311, A058673 (labeled matroids), A283877, A298422, A306017, A306018, A306019, A306021.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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