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A294589 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*x^j)^(j^k).

%I A294589 #19 Nov 04 2017 10:55:02
%S A294589 1,1,1,1,1,3,1,1,5,6,1,1,9,14,14,1,1,17,36,42,25,1,1,33,98,140,103,56,
%T A294589 1,1,65,276,498,481,289,97,1,1,129,794,1844,2419,1774,690,198,1,1,257,
%U A294589 2316,7002,12745,12173,5925,1771,354,1,1,513,6818,27020,69283,89706,56974,20076,4206,672,1
%N A294589 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*x^j)^(j^k).
%H A294589 Seiichi Manyama, <a href="/A294589/b294589.txt">Antidiagonals n = 0..139, flattened</a>
%F A294589 A(0,k) = 1 and A(n,k) = (1/n) * Sum_{j=1..n} (Sum_{d|j} d^(k+1+j/d)) * A(n-j,k) for n > 0.
%e A294589 Square array begins:
%e A294589     1,  1,   1,   1,    1, ...
%e A294589     1,  1,   1,   1,    1, ...
%e A294589     3,  5,   9,  17,   33, ...
%e A294589     6, 14,  36,  98,  276, ...
%e A294589    14, 42, 140, 498, 1844, ...
%Y A294589 Columns k=0..3 give A006906, A266941, A285241, A294590.
%Y A294589 Rows n=0-1 give A000012.
%Y A294589 Cf. A144048, A294587.
%K A294589 nonn,tabl
%O A294589 0,6
%A A294589 _Seiichi Manyama_, Nov 03 2017