login
Number of linear extensions of the one-level grid poset G[(2^n), (0^(n-1)), (0^(n-1))].
1

%I #17 Dec 15 2016 16:57:23

%S 1,20,1301,177260,41385102,14760468600,7465847167005,5083351577582300,

%T 4483012419041095680,4971032496120058085376,6769339545226095791964160,

%U 11105730970797793499164966912,21604722570792867452576610648064

%N Number of linear extensions of the one-level grid poset G[(2^n), (0^(n-1)), (0^(n-1))].

%C The definition of a one-level grid poset can be found in the Pan links. The number of linear extensions of the one-level grid poset G[(0^n), (0^(n-1)), (0^(n-1))] is given by the Catalan number A000108(n) and the number of linear extensions of the one-level grid poset G[(1^n), (0^(n-1)), (0^(n-1))] is given by A274644(n).

%H Ran Pan, <a href="http://www.math.ucsd.edu/~projectp/problems/p1.html">Problem 1</a>, Project P.

%H Ran Pan, <a href="http://www.math.ucsd.edu/~projectp/problems/solutions/OneLevelGridPoset.pdf">Algorithmic Solution to Problem 1 (and linear extensions of general one-level grid-like posets)</a>, Project P.

%Y Cf. A000108, A274644.

%K nonn

%O 1,2

%A _Ran Pan_, Jun 30 2016