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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. 6

%I

%S 1,3,1,8,6,1,24,25,10,1,83,98,63,15,1,324,399,338,135,21,1,1400,1746,

%T 1727,980,257,28,1,6609,8271,8874,6426,2455,448,36,1,33758,42284,

%U 47191,40334,20506,5474,730,45,1,185136,231939,263458,250839,158827,57239,11128,1128,55,1

%N 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 Alois P. Heinz, <a href="/A286416/b286416.txt">Rows n = 1..141, flattened</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%e 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 Triangle T(n,k) begins:

%e : 1;

%e : 3, 1;

%e : 8, 6, 1;

%e : 24, 25, 10, 1;

%e : 83, 98, 63, 15, 1;

%e : 324, 399, 338, 135, 21, 1;

%e : 1400, 1746, 1727, 980, 257, 28, 1;

%e : 6609, 8271, 8874, 6426, 2455, 448, 36, 1;

%Y Columns k=1-2 give: A038561 (for n>1), A286433.

%Y Main diagonal and first lower diagonal give: A000012, A000217.

%Y Row sums give A070071.

%Y Cf. A000110, A130534, A270236, A286232.

%K nonn,tabl

%O 1,2

%A _Alois P. Heinz_, May 08 2017

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Last modified February 20 20:31 EST 2020. Contains 332084 sequences. (Running on oeis4.)