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A286416 Number T(n,k) of entries in the k-th last blocks of all set partitions of [n]; triangle T(n,k), n>=1, 1<=k<=n, read by rows.

%I A286416 #17 Aug 03 2021 15:02:23
%S A286416 1,3,1,8,6,1,24,25,10,1,83,98,63,15,1,324,399,338,135,21,1,1400,1746,
%T A286416 1727,980,257,28,1,6609,8271,8874,6426,2455,448,36,1,33758,42284,
%U A286416 47191,40334,20506,5474,730,45,1,185136,231939,263458,250839,158827,57239,11128,1128,55,1
%N A286416 Number T(n,k) of entries in the k-th last blocks of all set partitions of [n]; triangle T(n,k), n>=1, 1<=k<=n, read by rows.
%H A286416 Alois P. Heinz, <a href="/A286416/b286416.txt">Rows n = 1..141, flattened</a>
%H A286416 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%e A286416 T(3,2) = 6 because the number of entries in the second last blocks of all set partitions of [3] (123, 12|3, 13|2, 1|23, 1|2|3) is 0+2+2+1+1 = 6.
%e A286416 Triangle T(n,k) begins:
%e A286416      1;
%e A286416      3,    1;
%e A286416      8,    6,    1;
%e A286416     24,   25,   10,    1;
%e A286416     83,   98,   63,   15,    1;
%e A286416    324,  399,  338,  135,   21,   1;
%e A286416   1400, 1746, 1727,  980,  257,  28,  1;
%e A286416   6609, 8271, 8874, 6426, 2455, 448, 36, 1;
%e A286416   ...
%Y A286416 Columns k=1-2 give: A038561 (for n>1), A286433.
%Y A286416 Main diagonal and first lower diagonal give: A000012, A000217.
%Y A286416 Row sums give A070071.
%Y A286416 Cf. A000110, A130534, A270236, A286232.
%K A286416 nonn,tabl
%O A286416 1,2
%A A286416 _Alois P. Heinz_, May 08 2017