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%I #12 Oct 29 2021 16:48:09
%S 2,3,6,17,96,2111,1114238,68723671293,1180735735906024030716,
%T 170141183460507917357914971986913657851,
%U 7237005577335553223087828975127304179197147198604070555943173844710572689402
%N Sum_{i=0..n} { 2^C(n,i) } - n.
%C Abstract simplicial complexes with n vertices for which all facets have the same dimension
%e There are 20 abstract simplicial complexes with 3 vertices; of these, all facets are the same dimension except for the 3 consisting of a line and a point such as {{1,2}, {3}}, so a(3)=17.
%t Table[Sum[2^Binomial[n,i],{i,0,n}]-n,{n,0,12}] (* _Harvey P. Dale_, Oct 29 2021 *)
%o (PARI) a(n) = sum(i=0, n, 2^binomial(n, i)) - n; \\ _Michel Marcus_, Aug 23 2013
%Y Cf. A000372(n) is the count over n vertices when we don't restrict to facets of the same dimension.
%K easy,nonn
%O 0,1
%A _Hugo van der Sanden_, Aug 10 2010
%E Edited by _N. J. A. Sloane_, Aug 10 2010
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