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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
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 (list; table; graph; refs; listen; history; text; internal format)
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: A123965 A124025 A257488 * A005295 A077897 A308737

Adjacent sequences:  A286413 A286414 A286415 * A286417 A286418 A286419

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, May 08 2017

STATUS

approved

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Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)