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.

1, 3, 1, 8, 6, 1, 24, 25, 10, 1, 83, 98, 63, 15, 1, 324, 399, 338, 135, 21, 1, 1400, 1746, 1727, 980, 257, 28, 1, 6609, 8271, 8874, 6426, 2455, 448, 36, 1, 33758, 42284, 47191, 40334, 20506, 5474, 730, 45, 1, 185136, 231939, 263458, 250839, 158827, 57239, 11128, 1128, 55, 1

Offset: 1

Author

Alois P. Heinz, May 08 2017

Keywords

• nonn
• tabl

Examples

			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.
Triangle T(n,k) begins:
     1;
     3,    1;
     8,    6,    1;
    24,   25,   10,    1;
    83,   98,   63,   15,    1;
   324,  399,  338,  135,   21,   1;
  1400, 1746, 1727,  980,  257,  28,  1;
  6609, 8271, 8874, 6426, 2455, 448, 36, 1;
  ...
		

Links

• Alois P. Heinz, Rows n = 1..141, flattened
• Wikipedia, Partition of a set

Crossrefs

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

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

Row sums give A070071.

Cf. A000110, A130534, A270236, A286232.