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A292717 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.

%I A292717 #6 Sep 21 2017 20:01:41
%S A292717 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 A292717 1,11,74,342,1044,1764,720,0,1,13,107,638,2754,8028,13068,5040,0,1,15,
%U A292717 146,1066,5944,24552,69264,109584,40320,0,1,17,191,1650,11274,60216,241128,663696,1026576,362880
%N A292717 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 A292717 E.g.f. of column k: -log(1 - x)/(1 - x)^k.
%e A292717 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 A292717 Square array begins:
%e A292717    0,    0,     0,     0,     0,      0,  ...
%e A292717    1,    1,     1,     1,     1,      1,  ...
%e A292717    1,    3,     5,     7,     9,     11,  ...
%e A292717    2,   11,    26,    47,    74,    107,  ...
%e A292717    6,   50,   154,   342,   638,   1066,  ...
%e A292717   24,  274,  1044,  2754,  5944,  11274,  ...
%t A292717 Table[Function[k, n! SeriesCoefficient[-Log[1 - x]/(1 - x)^k, {x, 0, n}]][j - n], {j, 0, 10}, {n, 0, j}] // Flatten
%Y A292717 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 A292717 Rows n=0..3 give  A000004, A000012, A005408, A080663 (with offset 0).
%Y A292717 Main diagonal gives A058806.
%K A292717 nonn,tabl
%O A292717 0,9
%A A292717 _Ilya Gutkovskiy_, Sep 21 2017