help with a new sequence

[franktaw at netscape.net]

This is A008284, a famous function.

Franklin T. Adams-Watters


-----Original Message-----
From: pauldhanna at juno.com

Seqfans,
      Row n of a related triangle could count the number of terms in 
row n
of Emerics triangle that sum to form the respective terms of the 
Narayana triangle.
 
This triangle P would begin:
1;
1, 1;
1, 1, 1;
1, 2, 1, 1;
1, 2, 2, 1, 1; ...

where row sums equal the partition numbers.
 
For example, row 3 of P is [1, 2, 1, 1]
since Narayana row 3 is [1, 4+2, 6, 1]
formed from row 3 of Emerics triangle: [1, 4, 2, 6, 1].
 
Is the resulting partition-related triangle P already in the OEIS?

It might have an interesting matrix inverse.
    Paul
 
-- Emeric Deutsch <deutsch at duke.poly.edu> wrote:
...
Triangle starts:
1;
1,1;
1,3,1;
1,4,2,6,1;
1,5,5,10,10,10,1;

Row n has A000041(n) terms (=number of partitions of n).
...
Thanks, Emeric




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