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A304871 Triangle read by rows: T(n, k) gives the number of partitions (d1,d2,...,dm) of n such that k = d1/1 <= d2/2 <= ... <= dm/m for 1 <= k <= n.

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%I A304871 #16 May 21 2018 09:55:06
%S A304871 1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,2,1,0,0,0,1,2,1,0,0,0,0,1,2,1,0,0,0,0,
%T A304871 0,1,3,1,1,0,0,0,0,0,1,4,1,1,0,0,0,0,0,0,1,5,1,1,0,0,0,0,0,0,0,1,5,2,
%U A304871 1,1,0,0,0,0,0,0,0,1,6,2,1,1,0,0,0,0,0,0,0,0,1
%N A304871 Triangle read by rows: T(n, k) gives the number of partitions (d1,d2,...,dm) of n such that k = d1/1 <= d2/2 <= ... <= dm/m for 1 <= k <= n.
%H A304871 Seiichi Manyama, <a href="/A304871/b304871.txt">Rows n = 1..100, flattened</a>
%e A304871 The partitions (d1,d2,...,dm) of 9 such that 1 = d1/1 <= d2/2 <= ... <= dm/m are (1, 8), (1, 2, 6) and (1, 3, 5). So T(9, 1) = 3.
%e A304871 First few rows are:
%e A304871   1;
%e A304871   0, 1;
%e A304871   1, 0, 1;
%e A304871   1, 0, 0, 1;
%e A304871   1, 0, 0, 0, 1;
%e A304871   2, 1, 0, 0, 0, 1;
%e A304871   2, 1, 0, 0, 0, 0, 1;
%e A304871   2, 1, 0, 0, 0, 0, 0, 1;
%e A304871   3, 1, 1, 0, 0, 0, 0, 0, 1;
%e A304871   4, 1, 1, 0, 0, 0, 0, 0, 0, 1;
%Y A304871 Row sums give A053282.
%Y A304871 Cf. A304869.
%K A304871 nonn,tabl
%O A304871 1,16
%A A304871 _Seiichi Manyama_, May 20 2018