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A304869 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).

%I A304869 #16 May 21 2018 10:17:39
%S A304869 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 A304869 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 A304869 11,9,3,1,7,13,10,4,1,1,7,14,12,5,1,1,7,15,14,6,1
%N A304869 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 A304869 Seiichi Manyama, <a href="/A304869/b304869.txt">Rows n = 1..100, flattened</a>
%e A304869 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 A304869 First few rows are:
%e A304869   1;
%e A304869   1;
%e A304869   1, 1;
%e A304869   1, 1;
%e A304869   1, 1;
%e A304869   1, 2, 1;
%e A304869   1, 2, 1;
%e A304869   1, 2, 1;
%e A304869   1, 3, 2;
%e A304869   1, 3, 2, 1;
%e A304869   1, 3, 3, 1;
%e A304869   1, 4, 4, 1;
%e A304869   1, 4, 4, 2;
%e A304869   1, 4, 5, 2;
%e A304869   1, 5, 6, 3, 1;
%Y A304869 Row sums give A053282.
%Y A304869 Cf. A304871.
%K A304869 nonn,tabf
%O A304869 1,10
%A A304869 _Seiichi Manyama_, May 20 2018