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Triangle read by rows: T(n, k) gives the number of partitions (d1,d2,...,dk) of n such that 0 < d1/1 <= d2/2 <= ... <= dk/k for 1 <= k <= A003056(n).
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%I #16 May 21 2018 10:17:39

%S 1,1,1,1,1,1,1,1,1,2,1,1,2,1,1,2,1,1,3,2,1,3,2,1,1,3,3,1,1,4,4,1,1,4,

%T 4,2,1,4,5,2,1,5,6,3,1,1,5,7,4,1,1,5,8,5,1,1,6,9,6,2,1,6,10,7,2,1,6,

%U 11,9,3,1,7,13,10,4,1,1,7,14,12,5,1,1,7,15,14,6,1

%N Triangle read by rows: T(n, k) gives the number of partitions (d1,d2,...,dk) of n such that 0 < d1/1 <= d2/2 <= ... <= dk/k for 1 <= k <= A003056(n).

%H Seiichi Manyama, <a href="/A304869/b304869.txt">Rows n = 1..100, flattened</a>

%e The partitions (d1,d2) of 9 such that 0 < d1/1 <= d2/2 are (1, 8), (2, 7) and (3, 6). So T(9, 2) = 3.

%e First few rows are:

%e 1;

%e 1;

%e 1, 1;

%e 1, 1;

%e 1, 1;

%e 1, 2, 1;

%e 1, 2, 1;

%e 1, 2, 1;

%e 1, 3, 2;

%e 1, 3, 2, 1;

%e 1, 3, 3, 1;

%e 1, 4, 4, 1;

%e 1, 4, 4, 2;

%e 1, 4, 5, 2;

%e 1, 5, 6, 3, 1;

%Y Row sums give A053282.

%Y Cf. A304871.

%K nonn,tabf

%O 1,10

%A _Seiichi Manyama_, May 20 2018