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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
OFFSET
1,2
LINKS
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.
Sequence in context: A125662 A124025 A257488 * A340672 A005295 A077897
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, May 08 2017
STATUS
approved