Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #15 Nov 13 2017 13:26:43
%S 1,1,1,1,1,3,1,1,5,12,1,1,9,32,82,1,1,17,90,304,725,1,1,33,260,1162,
%T 3537,8811,1,1,65,762,4516,17435,52010,128340,1,1,129,2252,17722,
%U 86529,310193,895397,2257687,1,1,257,6690,69964,431675,1865766,6286826,18016416,45658174
%N Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of exp(Sum_{j>0} sigma_k(j)*x^j/j) in powers of x.
%F G.f. of column k: Product_{j>0} 1/(1 - j^j*x^j)^(j^(k-1)).
%e Square array begins:
%e 1, 1, 1, 1, 1, ...
%e 1, 1, 1, 1, 1, ...
%e 3, 5, 9, 17, 33, ...
%e 12, 32, 90, 260, 762, ...
%e 82, 304, 1162, 4516, 17722, ...
%e 725, 3537, 17435, 86529, 431675, ...
%Y Columns k=0..2 give A023881, A023882, A294813.
%Y Rows n=0+1, 2 give A000012, A000051(n+1).
%Y Cf. A294296, A294947.
%K nonn,tabl
%O 0,6
%A _Seiichi Manyama_, Nov 11 2017