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

Author

Gus Wiseman, Jun 18 2018

Keywords

• nonn
• tabl

Examples

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

Links

• Wikipedia, Hypergraph

Crossrefs

Second column is A001187. Row sums are A299353.

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

Programs

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}]

Formula

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