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%I #14 May 09 2021 10:02:46
%S 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,
%T 11,14,25,36,58,69,165,22,15,22,35,60,87,138,165,393,937,42,30,44,75,
%U 132,203,345,495,786,937,2233,56,42,60,110,180,319,483,825,1179,1874,2233,5322
%N Eigentriangle of A027293.
%C 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.
%C For another definition of L-eigen-matrix of A027293 see A343234. - _Wolfdieter Lang_, Apr 16 2021
%F Triangle read by rows, A027293 * (A067687 * 0^(n-k)); 1 <= k <= n. (A067687 * 0^(n-k)) = 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, ...).
%e The triangle begins:
%e n \ k 1 2 3 4 5 6 7 8 9 10 11 ...
%e -------------------------------------------
%e 1: 1
%e 2: 1 1
%e 3: 2 1 2
%e 4: 3 2 2 5
%e 5: 5 3 4 5 12
%e 6: 7 5 6 10 12 29
%e 7: 11 7 10 15 24 29 69
%e 8: 15 11 14 25 36 58 69 165
%e 9: 22 15 22 35 60 87 138 165 393
%e 10: 30 22 30 55 84 145 207 330 393 937
%e 11: 42 30 44 75 132 203 345 495 786 937 2233
%e ... reformatted and extended by _Wolfdieter Lang_, May 02 2021
%e 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).
%Y Cf. A027293, A067687, A000041, A343234.
%K nonn,easy,tabl
%O 1,4
%A _Gary W. Adamson_, Sep 04 2008
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