A303940 - OEIS

%I #16 May 03 2018 08:52:31

%S 1,1,0,1,1,1,1,1,1,1,1,1,2,2,1,1,1,2,2,3,2,1,1,2,3,4,4,3,1,1,2,3,4,5,

%T 5,3,1,1,2,3,5,6,8,7,5,1,1,2,3,5,6,9,10,10,5,1,1,2,3,5,7,10,12,14,13,

%U 8,1,1,2,3,5,7,10,13,17,18,17,9,1,1,2,3,5,7,11,14,19,23,25,22,13

%N Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-x^(j*(j+k)))/(1-x^j). in powers of x.

%C A(n,k) is the number of partitions of n into at most 0+k copies of 1, 1+k copies of 2, 2+k copies of 3, ... .

%H Seiichi Manyama, <a href="/A303940/b303940.txt">Antidiagonals n = 0..139, flattened</a>

%e Square array begins:

%e    1, 1, 1, 1,  1,  1,  1,  1, ...

%e    0, 1, 1, 1,  1,  1,  1,  1, ...

%e    1, 1, 2, 2,  2,  2,  2,  2, ...

%e    1, 2, 2, 3,  3,  3,  3,  3, ...

%e    1, 3, 4, 4,  5,  5,  5,  5, ...

%e    2, 4, 5, 6,  6,  7,  7,  7, ...

%e    3, 5, 8, 9, 10, 10, 11, 11, ...

%Y Columns k=0..2 give A087153, A052335, A303939.

%Y Main diagonal gives A000041.

%K nonn,tabl

%O 0,13

%A _Seiichi Manyama_, May 03 2018