<html><P>Seqfans,<BR> Row n of a related triangle could count the number of terms in row n <BR>of Emerics triangle that sum to form the respective terms of the Narayana triangle. <BR> <BR>This triangle P would begin:<BR>1;<BR>1, 1;<BR>1, 1, 1;<BR>1, 2, 1, 1;<BR>1, 2, 2, 1, 1; ...<BR><BR>where row sums equal the partition numbers.<BR> <BR>For example, row 3 of P is [1, 2, 1, 1]<BR>since Narayana row 3 is [1, 4+2, 6, 1] <BR>formed from row 3 of Emerics triangle: [1, 4, 2, 6, 1].<BR> <BR>Is the resulting partition-related triangle P already in the OEIS?<BR><BR>It might have an interesting matrix inverse. <BR> Paul<BR> <BR>-- Emeric Deutsch <deutsch@duke.poly.edu> wrote:<BR>...<BR>Triangle starts:<BR>1;<BR>1,1;<BR>1,3,1;<BR>1,4,2,6,1;<BR>1,5,5,10,10,10,1;<BR><BR>Row n has A000041(n) terms (=number of partitions of n).<BR>...<BR>Thanks, Emeric<BR></P></html>