

A169974


Sum_{i=0..n} { 2^C(n,i) }  n.


0



2, 3, 6, 17, 96, 2111, 1114238, 68723671293, 1180735735906024030716, 170141183460507917357914971986913657851, 7237005577335553223087828975127304179197147198604070555943173844710572689402
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OFFSET

0,1


COMMENTS

Abstract simplicial complexes with n vertices for which all facets have the same dimension


LINKS



EXAMPLE

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.


MATHEMATICA

Table[Sum[2^Binomial[n, i], {i, 0, n}]n, {n, 0, 12}] (* Harvey P. Dale, Oct 29 2021 *)


PROG

(PARI) a(n) = sum(i=0, n, 2^binomial(n, i))  n; \\ Michel Marcus, Aug 23 2013


CROSSREFS

Cf. A000372(n) is the count over n vertices when we don't restrict to facets of the same dimension.


KEYWORD

easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



