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A294758 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^(k*j)*x^j) in powers of x.

%I A294758 #15 Nov 08 2017 09:15:21
%S A294758 1,1,1,1,1,2,1,1,5,3,1,1,17,32,5,1,1,65,746,304,7,1,1,257,19748,66538,
%T A294758 3537,11,1,1,1025,531698,16801060,9843827,52010,15,1,1,4097,14349932,
%U A294758 4295564530,30535638897,2188210276,895397,22,1,1,16385,387424586,1099527026284,95371863254051,101591953731770,680615495493,18016416,30
%N A294758 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^(k*j)*x^j) in powers of x.
%H A294758 Seiichi Manyama, <a href="/A294758/b294758.txt">Antidiagonals n = 0..52, flattened</a>
%F A294758 A(0,k) = 1 and A(n,k) = (1/n) * Sum_{j=1..n} (Sum_{d|j} d^(1+k*j)) * A(n-j,k) for n > 0.
%e A294758 Square array begins:
%e A294758    1,   1,     1,        1, ...
%e A294758    1,   1,     1,        1, ...
%e A294758    2,   5,    17,       65, ...
%e A294758    3,  32,   746,    19748, ...
%e A294758    5, 304, 66538, 16801060, ...
%Y A294758 Columns k=0..1 give A000041, A023882.
%Y A294758 Rows n=0-1 give A000012.
%Y A294758 Cf. A294653.
%K A294758 nonn,tabl
%O A294758 0,6
%A A294758 _Seiichi Manyama_, Nov 08 2017