A299354 Regular triangle where T(n,k) is the number of labeled connected k-uniform hypergraphs spanning n vertices.

1, 0, 1, 0, 4, 1, 0, 38, 11, 1, 0, 728, 958, 26, 1, 0, 26704, 1042632, 32596, 57, 1, 0, 1866256, 34352418950, 34359509614, 2096731, 120, 1, 0, 251548592, 72057319189266922, 1180591620442534312262, 72057594021152435, 268434467, 247, 1, 0, 66296291072

Offset

1,5

Links

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

Wikipedia, Hypergraph

Formula

Column k is the logarithmic transform of the inverse binomial transform of c(d) = 2^binomial(d,k).

Example

Triangle begins:
1
0, 1
0, 4, 1
0, 38, 11, 1
0, 728, 958, 26, 1
0, 26704, 1042632, 32596, 57, 1

Mathematica

nn=10; Table[SeriesCoefficient[Log[Sum[x^n/n!*Sum[(-1)^(n-d)*Binomial[n, d]*2^Binomial[d, k], {d, 0, n}], {n, 0, nn}]], {x, 0, n}]*n!, {n, nn}, {k, n}]

Crossrefs

Second column is A001187. Row sums are A299353.

Cf. A000005, A001315, A006126, A006129, A038041, A048143, A298422, A299353, A299471, A306020, A306021.

Sequence in context: A246609 A371080 A130636 * A117414 A085639 A158972

Adjacent sequences: A299351 A299352 A299353 * A299355 A299356 A299357

Keyword

nonn,tabl

Author

Gus Wiseman, Jun 18 2018

Status

approved