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