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

1,2

Links

Alois P. Heinz, Rows n = 1..141, flattened

Wikipedia, Partition of a set

Example

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;
  ...

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.

Sequence in context: A125662 A124025 A257488 * A340672 A005295 A077897

Adjacent sequences: A286413 A286414 A286415 * A286417 A286418 A286419

Keyword

nonn,tabl

Author

Alois P. Heinz, May 08 2017

Status

approved