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A294582 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1 - j^k*x^j)^j.

%I A294582 #16 Nov 04 2017 08:11:06
%S A294582 1,1,1,1,1,3,1,1,5,6,1,1,9,14,13,1,1,17,36,42,24,1,1,33,98,148,103,48,
%T A294582 1,1,65,276,546,489,289,86,1,1,129,794,2068,2467,1959,690,160,1,1,257,
%U A294582 2316,7962,12969,14281,6326,1771,282,1,1,513,6818,30988,70243
%N A294582 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1 - j^k*x^j)^j.
%H A294582 Seiichi Manyama, <a href="/A294582/b294582.txt">Antidiagonals n = 0..139, flattened</a>
%F A294582 A(0,k) = 1 and A(n,k) = (1/n) * Sum_{j=1..n} (Sum_{d|j} d^(2+k*j/d)) * A(n-j,k) for n > 0.
%e A294582 Square array begins:
%e A294582     1,  1,   1,   1,    1, ...
%e A294582     1,  1,   1,   1,    1, ...
%e A294582     3,  5,   9,  17,   33, ...
%e A294582     6, 14,  36,  98,  276, ...
%e A294582    13, 42, 148, 546, 2068, ...
%Y A294582 Columns k=0..2 give A000219, A266941, A285674.
%Y A294582 Rows n=0-1 give A000012.
%Y A294582 Cf. A292193, A294580.
%K A294582 nonn,tabl
%O A294582 0,6
%A A294582 _Seiichi Manyama_, Nov 02 2017