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A299471
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Regular triangle where T(n,k) is the number of labeled k-uniform hypergraphs spanning n vertices.
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17
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1, 1, 1, 1, 4, 1, 1, 41, 11, 1, 1, 768, 958, 26, 1, 1, 27449, 1042642, 32596, 57, 1, 1, 1887284, 34352419335, 34359509614, 2096731, 120, 1, 1, 252522481, 72057319189324805, 1180591620442534312297, 72057594021152435, 268434467, 247, 1, 1, 66376424160
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OFFSET
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1,5
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LINKS
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FORMULA
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T(n, k) = Sum_{d = 0..n} (-1)^(n-d)*binomial(n,d)*2^binomial(d,k).
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 4, 1;
1, 41, 11, 1;
1, 768, 958, 26, 1;
1, 27449, 1042642, 32596, 57, 1;
...
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MATHEMATICA
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Table[Sum[(-1)^(n-d)*Binomial[n, d]*2^Binomial[d, k], {d, 0, n}], {n, 10}, {k, n}]
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PROG
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(PARI) T(n, k) = sum(d = 0, n, (-1)^(n-d)*binomial(n, d)*2^binomial(d, k)) \\ Andrew Howroyd, Jan 16 2024
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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