

A143866


Eigentriangle of A027293.


1



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, 22, 15, 22, 35, 60, 87, 138, 165, 393
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OFFSET

1,4


COMMENTS

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 nth row terms = rightmost term of next row.


LINKS

Table of n, a(n) for n=1..45.


FORMULA

Triangle read by rows, A027293 * (A067687 * 0^(nk)); 1<=k<=n. (A067687 * 0^(nk)) = an infinite lower triangular 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,...).


EXAMPLE

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).


CROSSREFS

Cf. A027293, A067687, A000041.
Sequence in context: A132148 A237829 A159974 * A155002 A182413 A296664
Adjacent sequences: A143863 A143864 A143865 * A143867 A143868 A143869


KEYWORD

nonn


AUTHOR

Gary W. Adamson, Sep 04 2008


STATUS

approved



