%I #12 Nov 08 2017 12:03:09
%S 1,1,1,1,1,3,1,1,4,11,1,1,6,18,59,1,1,10,36,132,339,1,1,18,84,384,900,
%T 2629,1,1,34,216,1296,3240,10080,20677,1,1,66,588,4704,13800,56880,
%U 93240,202089,1,1,130,1656,17712,64440,386640,635040,1285200,2066201
%N Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: Product_{j>0} 1/(1-j^k*x^j)^(1/j).
%H Seiichi Manyama, <a href="/A294761/b294761.txt">Antidiagonals n = 0..139, flattened</a>
%F A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..n} (Sum_{d|j} d^(k*j/d)) * A(n-j,k)/(n-j)! for n > 0.
%e Square array begins:
%e 1, 1, 1, 1, 1, ...
%e 1, 1, 1, 1, 1, ...
%e 3, 4, 6, 10, 18, ...
%e 11, 18, 36, 84, 216, ...
%e 59, 132, 384, 1296, 4704, ...
%Y Columns k=0..1 give A028342, A294462.
%Y Rows n=0-1 give A000012.
%Y Cf. A294616.
%K nonn,tabl
%O 0,6
%A _Seiichi Manyama_, Nov 08 2017