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A322762 Irregular triangle read by rows: to get row n, take partitions of n ordered as in A080577, and in each partition, change each j-th occurrence of k to j; use compressed notation as in A322761.

%I A322762 #14 Feb 14 2019 19:18:31
%S A322762 1,1,12,1,11,123,1,11,12,112,1234,1,11,11,112,121,1123,12345,1,11,11,
%T A322762 112,12,111,1123,123,1212,11234,123456,1,11,11,112,11,111,1123,121,
%U A322762 112,1112,11234,1231,12123,112345,1234567,1,11,11,112,11,111,1123,12,111
%N A322762 Irregular triangle read by rows: to get row n, take partitions of n ordered as in A080577, and in each partition, change each j-th occurrence of k to j; use compressed notation as in A322761.
%D A322762 D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.2.1.5, Problem 73, pp. 415, 761.
%H A322762 Alois P. Heinz, <a href="/A322762/b322762.txt">Rows n = 1..28, flattened</a>
%e A322762 Triangle begins:
%e A322762   1,
%e A322762   1, 12,
%e A322762   1, 11, 123,
%e A322762   1, 11, 12, 112, 1234,
%e A322762   1, 11, 11, 112, 121, 1123, 12345,
%e A322762   1, 11, 11, 112, 12, 111, 1123, 123, 1212, 11234, 123456,
%e A322762   ...
%e A322762 For example, the 11 partitions of 6 are:
%e A322762 6, 51, 42, 411, 33, 321, 3111, 222, 2211, 21111, 111111,
%e A322762 and applying the transformation we get:
%e A322762 1, 11, 11, 112, 12, 111, 1123, 123, 1212, 11234, 123456.
%p A322762 b:= (n, i)-> `if`(n=0 or i=1, [cat($1..n)], [(t->
%p A322762     seq(map(x-> cat($1..(t+1-j), x), b(n-i*(t+1-j)
%p A322762     , i-1))[], j=1..t))(iquo(n, i)), b(n, i-1)[]]):
%p A322762 T:= n-> map(parse, b(n$2))[]:
%p A322762 seq(T(n), n=1..10);  # _Alois P. Heinz_, Dec 30 2018
%Y A322762 Cf. A080577, A066633, A322761, A322763.
%K A322762 nonn,tabf,look,base
%O A322762 1,3
%A A322762 _N. J. A. Sloane_, Dec 30 2018
%E A322762 More terms from _Alois P. Heinz_, Dec 30 2018