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A359107
Triangle read by rows, T(n, k) = Sum_{j=0..k} Stirling2(n, j) = Sum_{j=0..k} A048993(n, j).
2
1, 0, 1, 0, 1, 2, 0, 1, 4, 5, 0, 1, 8, 14, 15, 0, 1, 16, 41, 51, 52, 0, 1, 32, 122, 187, 202, 203, 0, 1, 64, 365, 715, 855, 876, 877, 0, 1, 128, 1094, 2795, 3845, 4111, 4139, 4140, 0, 1, 256, 3281, 11051, 18002, 20648, 21110, 21146, 21147
OFFSET
0,6
COMMENTS
T(n, k) is the number of partitions of an n-set that contain at most k nonempty subsets.
EXAMPLE
Triangle T(n, k) starts:
[0] [1]
[1] [0, 1]
[2] [0, 1, 2]
[3] [0, 1, 4, 5]
[4] [0, 1, 8, 14, 15]
[5] [0, 1, 16, 41, 51, 52]
[6] [0, 1, 32, 122, 187, 202, 203]
[7] [0, 1, 64, 365, 715, 855, 876, 877]
[8] [0, 1, 128, 1094, 2795, 3845, 4111, 4139, 4140]
[9] [0, 1, 256, 3281, 11051, 18002, 20648, 21110, 21146, 21147]
MAPLE
with(ListTools): ps := L -> PartialSums(L):
Flatten([seq(ps([seq(Stirling2(n, k), k = 0..n)]), n = 0..10)]);
CROSSREFS
Cf. A048993, A000110 (T(n, n)), A359355 (T(2*n, n)), A359109 (row sums).
Without column k=0 the same as A102661.
Sequence in context: A342134 A349740 A327117 * A229223 A128749 A106579
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Dec 27 2022
STATUS
approved