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A286232 Sum T(n,k) of the 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. 4
1, 5, 1, 19, 10, 1, 75, 57, 17, 1, 323, 285, 145, 26, 1, 1512, 1421, 975, 317, 37, 1, 7630, 7395, 5999, 2865, 616, 50, 1, 41245, 40726, 36183, 22411, 7315, 1094, 65, 1, 237573, 237759, 221689, 163488, 72581, 16630, 1812, 82, 1, 1451359, 1468162, 1405001, 1160764, 649723, 206249, 34425, 2840, 101, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Rows n = 1..100, flattened

Wikipedia, Partition of a set

EXAMPLE

T(3,2) = 10 because the sum of the entries in the second last blocks of all set partitions of [3] (123, 12|3, 13|2, 1|23, 1|2|3) is 0+3+4+1+2 = 10.

Triangle T(n,k) begins:

:     1;

:     5,     1;

:    19,    10,     1;

:    75,    57,    17,     1;

:   323,   285,   145,    26,    1;

:  1512,  1421,   975,   317,   37,    1;

:  7630,  7395,  5999,  2865,  616,   50,  1;

: 41245, 40726, 36183, 22411, 7315, 1094, 65, 1;

CROSSREFS

Column k=1 gives A285424.

Main diagonal and first lower diagonal give: A000012, A002522.

Row sums give A000110(n) * A000217(n) = A105488(n+3).

Cf. A285362, A286231, A286416.

Sequence in context: A193861 A193857 A146055 * A147437 A147369 A066480

Adjacent sequences:  A286229 A286230 A286231 * A286233 A286234 A286235

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, May 04 2017

STATUS

approved

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Last modified February 22 12:00 EST 2020. Contains 332135 sequences. (Running on oeis4.)