A349782 Triangle read by rows, T(n, k) = Sum_{j=0..k} |Stirling1(n, j)|.
1, 0, 1, 0, 1, 2, 0, 2, 5, 6, 0, 6, 17, 23, 24, 0, 24, 74, 109, 119, 120, 0, 120, 394, 619, 704, 719, 720, 0, 720, 2484, 4108, 4843, 5018, 5039, 5040, 0, 5040, 18108, 31240, 38009, 39969, 40291, 40319, 40320, 0, 40320, 149904, 268028, 335312, 357761, 362297, 362843, 362879, 362880
Offset: 0
Examples
Triangle starts: [0] 1; [1] 0, 1; [2] 0, 1, 2; [3] 0, 2, 5, 6; [4] 0, 6, 17, 23, 24; [5] 0, 24, 74, 109, 119, 120; [6] 0, 120, 394, 619, 704, 719, 720; [7] 0, 720, 2484, 4108, 4843, 5018, 5039, 5040; [8] 0, 5040, 18108, 31240, 38009, 39969, 40291, 40319, 40320;
Crossrefs
Programs
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Maple
T := (n, k) -> add(abs(Stirling1(n,j)), j = 0..k): seq(seq(T(n, k), k = 0..n), n = 0..9);
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Mathematica
T[n_, k_] := Sum[Abs[StirlingS1[n, j]], {j, 0, k}]; Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Amiram Eldar, Dec 09 2021 *) -
PARI
T(n, k) = sum(j=0, k, abs(stirling(n, j, 1))); \\ Michel Marcus, Dec 09 2021
Formula
T(n,k) = Sum_{j=0..k} A132393(n,j). - Alois P. Heinz, Dec 10 2021
Comments