1,4

Left border = partition numbers, A000041 starting (1, 1, 2, 3, 5, 7,...). Right border = INVERT transform of partition numbers starting (1, 1, 2, 5, 12,...); with row sums the same sequence but starting (1, 2, 5, 12,...). Sum of n-th row terms = rightmost term of next row.

Triangle read by rows, A027293 * (A067687 * 0^(n-k)); 1<=k<=n. (A067687 * 0^(n-k)) = an infinite lower trianglular matrix with the INVERT transform of the partition function as the main diagonal: (1, 1, 2, 5, 12, 29, 69, 165,...); and the rest zeros. Triangle A027293 = n terms of "partition numbers decrescendo"; By rows = termwise product of n terms of partition decrescendo and n terms of A027293: (1, 1, 2, 5, 12, 29, 69, 165,...).

First few rows of the triangle = 1; 1, 1; 2, 1, 2; 3, 2, 2, 5; 5, 3, 4, 5, 12; 7, 5, 6, 10, 12, 29; 11, 7, 10, 15, 24, 29, 69; 15, 11, 14, 25, 36, 58, 69, 165; ... Row 4 = (3, 2, 2, 5) = termwise product of (3, 2, 1, 1) and (1, 1, 2, 5) = (3*1, 2*1, 1*2, 1*5).

A027293, Cf. A067687, A000041

Sequence in context: A112218 A132148 A159974 this_sequence A155002 A103342 A147784

Adjacent sequences: A143863 A143864 A143865 this_sequence A143867 A143868 A143869

nonn

Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 04 2008