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A286231 Sum T(n,k) of the entries in the k-th last cycles of all permutations of [n]; triangle T(n,k), n>=1, 1<=k<=n, read by rows.

%I A286231 #13 Aug 21 2021 06:35:59
%S A286231 1,5,1,25,10,1,143,79,17,1,942,634,197,26,1,7074,5462,2129,417,37,1,
%T A286231 59832,51214,23381,5856,786,50,1,563688,523386,269033,80053,13934,
%U A286231 1360,65,1,5858640,5813892,3281206,1111498,232349,29728,2204,82,1
%N A286231 Sum T(n,k) of the entries in the k-th last cycles of all permutations of [n]; triangle T(n,k), n>=1, 1<=k<=n, read by rows.
%H A286231 Alois P. Heinz, <a href="/A286231/b286231.txt">Rows n = 1..20, flattened</a>
%H A286231 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%e A286231 T(3,2) = 10 because the sum of the entries in the second last cycles of all permutations of [3] ((123), (132), (12)(3), (13)(2), (1)(23), (1)(2)(3)) is 0+0+3+4+1+2 = 10.
%e A286231 Triangle T(n,k) begins:
%e A286231        1;
%e A286231        5,      1;
%e A286231       25,     10,      1;
%e A286231      143,     79,     17,     1;
%e A286231      942,    634,    197,    26,     1;
%e A286231     7074,   5462,   2129,   417,    37,    1;
%e A286231    59832,  51214,  23381,  5856,   786,   50,  1;
%e A286231   563688, 523386, 269033, 80053, 13934, 1360, 65, 1;
%e A286231   ...
%Y A286231 Column k=1 gives A285382.
%Y A286231 Main diagonal and first lower diagonal give: A000012, A002522.
%Y A286231 Row sums give A000142 * A000217 = A180119.
%Y A286231 Cf. A285793, A286232.
%K A286231 nonn,tabl
%O A286231 1,2
%A A286231 _Alois P. Heinz_, May 04 2017