A359107 Triangle read by rows, T(n, k) = Sum_{j=0..k} Stirling2(n, j) = Sum_{j=0..k} A048993(n, j).
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
Examples
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]
Crossrefs
Programs
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Maple
with(ListTools): ps := L -> PartialSums(L): Flatten([seq(ps([seq(Stirling2(n, k), k = 0..n)]), n = 0..10)]);
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