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A293525 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of e.g.f. Product_{j > 0, j mod k > 0} exp(x^j).

%I A293525 #26 Oct 15 2017 01:05:52
%S A293525 1,1,0,1,1,0,1,1,1,0,1,1,3,7,0,1,1,3,7,25,0,1,1,3,13,49,181,0,1,1,3,
%T A293525 13,49,321,1201,0,1,1,3,13,73,381,2131,10291,0,1,1,3,13,73,381,2971,
%U A293525 19783,97777,0,1,1,3,13,73,501,3331,26713,195777,1013545,0,1,1
%N A293525 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of e.g.f. Product_{j > 0, j mod k > 0} exp(x^j).
%H A293525 Seiichi Manyama, <a href="/A293525/b293525.txt">Antidiagonals n = 0..139, flattened</a>
%F A293525 E.g.f. of column k: exp((Sum_{j=1..k-1} x^j)/(1 - x^k)).
%e A293525 Square array begins:
%e A293525    1,   1,   1,   1,   1, ...
%e A293525    0,   1,   1,   1,   1, ...
%e A293525    0,   1,   3,   3,   3, ...
%e A293525    0,   7,   7,  13,  13, ...
%e A293525    0,  25,  49,  49,  73, ...
%e A293525    0, 181, 321, 381, 381, ...
%t A293525 kmax = 12; col[k_] := PadRight[(Exp[Sum[x^j, {j, 1, k - 1}]/(1 - x^k)] + O[x]^kmax // CoefficientList[#, x] &), kmax]*Range[0, kmax - 1]!; A = Array[col, kmax]; Table[A[[n - k + 1, k]], {n, 1, kmax}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Oct 12 2017, from formula *)
%Y A293525 Columns k=1..3 give A000007, A088009, A113775.
%Y A293525 Rows n=0 gives A000012.
%Y A293525 Main diagonal gives A000262.
%Y A293525 Cf. A293530.
%K A293525 nonn,tabl
%O A293525 0,13
%A A293525 _Seiichi Manyama_, Oct 11 2017