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A299471 Regular triangle where T(n,k) is the number of labeled k-uniform hypergraphs spanning n vertices. 14
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

Table of n, a(n) for n=1..38.

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 February 19 21:14 EST 2019. Contains 320328 sequences. (Running on oeis4.)