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A294579 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is Sum_{d|n} d^(1 + k*n/d).

%I A294579 #27 Jan 14 2023 08:44:31
%S A294579 1,1,3,1,5,4,1,9,10,7,1,17,28,25,6,1,33,82,97,26,12,1,65,244,385,126,
%T A294579 80,8,1,129,730,1537,626,588,50,15,1,257,2188,6145,3126,4508,344,161,
%U A294579 13,1,513,6562,24577,15626,35652,2402,2049,163,18
%N A294579 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is Sum_{d|n} d^(1 + k*n/d).
%H A294579 Seiichi Manyama, <a href="/A294579/b294579.txt">Antidiagonals n = 1..140, flattened</a>
%F A294579 L.g.f. of column k: -log(Product_{j>=1} (1 - j^k * x^j)). - _Seiichi Manyama_, Jun 02 2019
%F A294579 G.f. of column k: Sum_{j>0} j^(k+1) * x^j / (1 - j^k * x^j). - _Seiichi Manyama_, Jan 14 2023
%e A294579 Square array begins:
%e A294579   1,  1,   1,   1,    1, ...
%e A294579   3,  5,   9,  17,   33, ...
%e A294579   4, 10,  28,  82,  244, ...
%e A294579   7, 25,  97, 385, 1537, ...
%e A294579   6, 26, 126, 626, 3126, ...
%Y A294579 Columns k=0..2 give A000203, A078308, A294567.
%Y A294579 Rows k=0..1 give A000012, A000051(n+1).
%Y A294579 Cf. A292166, A292193.
%K A294579 nonn,tabl
%O A294579 1,3
%A A294579 _Seiichi Manyama_, Nov 02 2017