A304939 Number of labeled nonempty hypertrees (connected antichains with no cycles) spanning some subset of {1,...,n} without singleton edges.
1, 0, 1, 7, 51, 506, 6843, 118581, 2504855, 62370529, 1788082153, 57997339632, 2099638691439, 83922479506503, 3670657248913385, 174387350448735877, 8942472292255441103, 492294103555090048458, 28958704109012732921523
Offset: 0
Keywords
Examples
The a(3) = 7 hypertrees are the following:
{{1,2}}
{{1,3}}
{{2,3}}
{{1,2,3}}
{{1,2},{1,3}}
{{1,2},{2,3}}
{{1,3},{2,3}}
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..200
Crossrefs
Programs
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PARI
\\ here b(n) is A030019 with b(1)=0. b(n)=if(n<2, n==0, sum(i=0, n, stirling(n-1, i, 2)*n^(i-1))); a(n)=if(n<1, n==0, sum(k=1, n, binomial(n, k)*b(k))); \\ Andrew Howroyd, Aug 27 2018
Formula
a(n) = A305004(n) - 1 for n > 0. - Andrew Howroyd, Aug 27 2018