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A294761 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).

%I A294761 #12 Nov 08 2017 12:03:09
%S A294761 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 A294761 2629,1,1,34,216,1296,3240,10080,20677,1,1,66,588,4704,13800,56880,
%U A294761 93240,202089,1,1,130,1656,17712,64440,386640,635040,1285200,2066201
%N A294761 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 A294761 Seiichi Manyama, <a href="/A294761/b294761.txt">Antidiagonals n = 0..139, flattened</a>
%F A294761 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 A294761 Square array begins:
%e A294761     1,   1,   1,    1,    1, ...
%e A294761     1,   1,   1,    1,    1, ...
%e A294761     3,   4,   6,   10,   18, ...
%e A294761    11,  18,  36,   84,  216, ...
%e A294761    59, 132, 384, 1296, 4704, ...
%Y A294761 Columns k=0..1 give A028342, A294462.
%Y A294761 Rows n=0-1 give A000012.
%Y A294761 Cf. A294616.
%K A294761 nonn,tabl
%O A294761 0,6
%A A294761 _Seiichi Manyama_, Nov 08 2017