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A349782
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Triangle read by rows, T(n, k) = Sum_{j=0..k} |Stirling1(n, j)|.
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1
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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
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OFFSET
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0,6
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COMMENTS
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T(n, k) is the number of permutations of n objects that contain at most k cycles.
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LINKS
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FORMULA
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EXAMPLE
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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;
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MAPLE
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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
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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 *)
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PROG
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(PARI) T(n, k) = sum(j=0, k, abs(stirling(n, j, 1))); \\ Michel Marcus, Dec 09 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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