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 A299471 Regular triangle where T(n,k) is the number of labeled k-uniform hypergraphs spanning n vertices. 13
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Wikipedia, Hypergraph FORMULA T(n, k) = Sum_{d = 0...n} (-1)^(n - d) binomial(n, d) 2^binomial(d, k). EXAMPLE Triangle begins: 1 1, 1 1, 4, 1 1, 41, 11, 1 1, 768, 958, 26, 1 1, 27449, 1042642, 32596, 57, 1 MATHEMATICA Table[Sum[(-1)^(n-d)*Binomial[n, d]*2^Binomial[d, k], {d, 0, n}], {n, 10}, {k, n}] CROSSREFS Second column is A006129. Third column is A302374. Row sums are A306021. Cf. A000005, A001315, A006126, A038041, A298422, A298426, A306017, A306018, A306019, A306020, A306021. Sequence in context: A158390 A228836 A176419 * A102602 A156951 A121066 Adjacent sequences:  A299468 A299469 A299470 * A299472 A299473 A299474 KEYWORD nonn,tabl AUTHOR Gus Wiseman, Jun 18 2018 STATUS approved

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Last modified April 8 14:52 EDT 2020. Contains 333314 sequences. (Running on oeis4.)