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A304939 Number of labeled nonempty hypertrees (connected antichains with no cycles) spanning some subset of {1,...,n} without singleton edges. 2
1, 0, 1, 7, 51, 506, 6843, 118581, 2504855, 62370529, 1788082153, 57997339632, 2099638691439, 83922479506503, 3670657248913385, 174387350448735877, 8942472292255441103, 492294103555090048458, 28958704109012732921523 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200

FORMULA

a(n) = A305004(n) - 1 for n > 0. - Andrew Howroyd, Aug 27 2018

EXAMPLE

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}}

PROG

(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

CROSSREFS

Cf. A030019, A035053, A048143, A134954, A134955, A134956, A134957, A134959, A144959, A303838, A304867, A304911, A304912, A304918, A305004.

Sequence in context: A219306 A246572 A230883 * A293073 A081216 A198087

Adjacent sequences:  A304936 A304937 A304938 * A304940 A304941 A304942

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 21 2018

STATUS

approved

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Last modified August 7 17:44 EDT 2020. Contains 336278 sequences. (Running on oeis4.)