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%I #13 May 22 2020 13:11:26
%S 1,2,1,3,1,1,4,2,2,1,1,1,5,3,2,1,1,1,1,1,6,4,2,3,3,2,2,2,1,1,1,1,1,1,
%T 1,7,5,2,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1,8,6,2,5,3,4,4,4,2,2,3,3,2,2,
%U 2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,9,7,2,6,3,5,4,5,2,2,4,3,2,3,3,3,3,2,2
%N A shell model of partitions. Triangle read by rows: row n lists the parts of the last section of the set of partitions of n.
%C Row n lists the terms of row n of A138138, in decreasing order. See the integrated diagram of partitions and more information in the entry A138138.
%H Robert Price, <a href="/A138151/b138151.txt">Table of n, a(n) for n = 1..4630, 20 rows.</a>
%e Triangle begins:
%e 1
%e 2,1
%e 3,1,1
%e 4,2,2,1,1,1
%e 5,3,2,1,1,1,1,1,
%e 6,4,2,3,3,2,2,2,1,1,1,1,1,1,1
%e 7,5,2,4,3,3,2,2,1,1,1,1,1,1,1,1,1,1,1
%e 8,6,2,5,3,4,4,4,2,2,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%e 9,7,2,6,3,5,4,5,2,2,4,3,2,3,3,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%t Table[Cases[IntegerPartitions[n], x_ /; Last[x] != 1] ~Join~ConstantArray[{1}, PartitionsP[n - 1]], {n, 8}] // Flatten (* _Robert Price_, May 22 2020 *)
%Y Cf. A135010, A138121, A138122, A138123, A138136, A138137, A138138, A138152, A138153.
%K nonn,tabf,less
%O 1,2
%A _Omar E. Pol_, Mar 21 2008
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