%I #6 Sep 21 2017 20:01:41
%S 0,0,1,0,1,1,0,1,3,2,0,1,5,11,6,0,1,7,26,50,24,0,1,9,47,154,274,120,0,
%T 1,11,74,342,1044,1764,720,0,1,13,107,638,2754,8028,13068,5040,0,1,15,
%U 146,1066,5944,24552,69264,109584,40320,0,1,17,191,1650,11274,60216,241128,663696,1026576,362880
%N Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. -log(1 - x)/(1 - x)^k.
%F E.g.f. of column k: -log(1 - x)/(1 - x)^k.
%e E.g.f. of column k: A_k(x) = x/1! + (2*k + 1)*x^2/2! + (3*k^2 + 6*k + 2)*x^3/3! + 2*(2*k^3 + 9*k^2 + 11*k + 3)*x^4/4! + ...
%e Square array begins:
%e 0, 0, 0, 0, 0, 0, ...
%e 1, 1, 1, 1, 1, 1, ...
%e 1, 3, 5, 7, 9, 11, ...
%e 2, 11, 26, 47, 74, 107, ...
%e 6, 50, 154, 342, 638, 1066, ...
%e 24, 274, 1044, 2754, 5944, 11274, ...
%t Table[Function[k, n! SeriesCoefficient[-Log[1 - x]/(1 - x)^k, {x, 0, n}]][j - n], {j, 0, 10}, {n, 0, j}] // Flatten
%Y Columns k=0..11 give A104150, A000254, A001705, A001711 (with offset 1), A001716 (with offset 1), A001721 (with offset 1), A051524, A051545, A051560, A051562, A051564, A203147.
%Y Rows n=0..3 give A000004, A000012, A005408, A080663 (with offset 0).
%Y Main diagonal gives A058806.
%K nonn,tabl
%O 0,9
%A _Ilya Gutkovskiy_, Sep 21 2017
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