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A115965 Number of planar subpartitions of size n pyramidal planar partition. 0

%I

%S 1,2,9,96,2498,161422,26217833,10794429504

%N Number of planar subpartitions of size n pyramidal planar partition.

%C This is a 2-dimensional analog of the Catalan numbers C_n (A000108). The number of subpartitions of the triangular partition [n,n-1,...,1] is C_{n+1}. The planar partition having its subpartitions counted is:

%C n n-1 ... 2 1

%C n-1 n-2 ... 1

%C ... ...

%C 2 1

%C 1

%H Oleg Lazarev, Matt Mizuhara, Ben Reid, <a href="http://www.math.oregonstate.edu/~swisherh/LazarevMizuharaReid.pdf">Some Results in Partitions, Plane Partitions, and Multipartitions</a>

%e The 9 planar subpartitions of [2,1|1] are [], [1], [2], [1,1], [1|1], [2,1], [2|1], [1,1|1] and [2,1|1] itself, so a(2)=9. (Here "," separates values on the same line and "|" separates lines.)

%Y Cf. A115728, A115729, A000219, A000108, A008793.

%K more,nonn

%O 0,2

%A _Franklin T. Adams-Watters_, Mar 14 2006

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Last modified January 28 13:27 EST 2020. Contains 331321 sequences. (Running on oeis4.)