A349782 - OEIS

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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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,6

COMMENTS

T(n, k) is the number of permutations of n objects that contain at most k cycles.

LINKS

Table of n, a(n) for n=0..54.

FORMULA

T(n,k) = Sum_{j=0..k} A132393(n,j). - Alois P. Heinz, Dec 10 2021

EXAMPLE

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;

MAPLE

T := (n, k) -> add(abs(Stirling1(n, j)), j = 0..k):

seq(seq(T(n, k), k = 0..n), n = 0..9);

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 *)

PROG

(PARI) T(n, k) = sum(j=0, k, abs(stirling(n, j, 1))); \\ Michel Marcus, Dec 09 2021

CROSSREFS

Row sums: A121586, central terms: A349783.

Cf. A132393, A048994, A008275, A000142, A033312, A000774, A081046, A130534.

Sequence in context: A301951 A144529 A319498 * A011297 A110282 A024308

Adjacent sequences: A349779 A349780 A349781 * A349783 A349784 A349785

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Dec 02 2021

STATUS

approved