



1, 2, 4, 9, 25, 88, 406, 2451, 19450, 202681, 2769965, 49519392, 1154411138, 34978238590, 1373171398361, 69648249299517, 4552778914494604
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OFFSET

0,2


COMMENTS

Partial sums of number of partially ordered sets ("posets") with n unlabeled elements. It is a law of small numbers example that this sequence, through the largest known terms, has three consecutive squares (4, 9, 25) and no primes other than 2.


LINKS

Table of n, a(n) for n=0..16.


FORMULA

a(n) = Sum_{i=0..n} A000112(i).


MATHEMATICA

Cases[Import["https://oeis.org/A000112/b000112.txt", "Table"], {_, _}][[All, 2]] // Accumulate (* JeanFrançois Alcover, Jan 01 2020 *)


CROSSREFS

Cf. A000112, A000798 (labeled topologies), A001035 (labeled posets), A001930 (unlabeled topologies), A006057, A079263, A079265.
Sequence in context: A192801 A270954 A173496 * A127055 A124835 A125799
Adjacent sequences: A173308 A173309 A173310 * A173312 A173313 A173314


KEYWORD

nonn,hard,more


AUTHOR

Jonathan Vos Post, Feb 16 2010


STATUS

approved



