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

%I A299354 #11 Jun 19 2018 12:36:05
%S A299354 1,0,1,0,4,1,0,38,11,1,0,728,958,26,1,0,26704,1042632,32596,57,1,0,
%T A299354 1866256,34352418950,34359509614,2096731,120,1,0,251548592,
%U A299354 72057319189266922,1180591620442534312262,72057594021152435,268434467,247,1,0,66296291072
%N A299354 Regular triangle where T(n,k) is the number of labeled connected k-uniform hypergraphs spanning n vertices.
%H A299354 Wikipedia, <a href="http://en.wikipedia.org/wiki/Hypergraph">Hypergraph</a>
%F A299354 Column k is the logarithmic transform of the inverse binomial transform of c(d) = 2^binomial(d,k).
%e A299354 Triangle begins:
%e A299354 1
%e A299354 0, 1
%e A299354 0, 4, 1
%e A299354 0, 38, 11, 1
%e A299354 0, 728, 958, 26, 1
%e A299354 0, 26704, 1042632, 32596, 57, 1
%t A299354 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}]
%Y A299354 Second column is A001187. Row sums are A299353.
%Y A299354 Cf. A000005, A001315, A006126, A006129, A038041, A048143, A298422, A299353, A299471, A306020, A306021.
%K A299354 nonn,tabl
%O A299354 1,5
%A A299354 _Gus Wiseman_, Jun 18 2018