A355006 Triangle read by rows. T(n, k) = n^(n - k) * |Stirling1(n, k)|.

1, 0, 1, 0, 2, 1, 0, 18, 9, 1, 0, 384, 176, 24, 1, 0, 15000, 6250, 875, 50, 1, 0, 933120, 355104, 48600, 3060, 90, 1, 0, 84707280, 29647548, 3899224, 252105, 8575, 147, 1, 0, 10569646080, 3425697792, 430309376, 27725824, 1003520, 20608, 224, 1

Offset

0,5

Links

Table of n, a(n) for n=0..44.

Example

Table T(n, k) begins:
[0] 1;
[1] 0,           1;
[2] 0,           2,          1;
[3] 0,          18,          9,         1;
[4] 0,         384,        176,        24,        1;
[5] 0,       15000,       6250,       875,       50,       1;
[6] 0,      933120,     355104,     48600,     3060,      90,     1;
[7] 0,    84707280,   29647548,   3899224,   252105,    8575,   147,   1;
[8] 0, 10569646080, 3425697792, 430309376, 27725824, 1003520, 20608, 224, 1;

Maple

seq(seq(n^(n - k)*abs(Stirling1(n, k)), k = 0..n), n = 0..9);

Mathematica

T[n_, k_] := If[n == k == 0, 1, n^(n - k) * Abs[StirlingS1[n, k]]]; Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Amiram Eldar, Jun 17 2022 *)

Crossrefs

A152684 (column 1), A006002 (subdiagonal), A092985 (row sums), A355007.

Sequence in context: A202700 A024026 A380252 * A269946 A009829 A202697

Adjacent sequences: A355003 A355004 A355005 * A355007 A355008 A355009

Keyword

nonn,tabl

Author

Peter Luschny, Jun 17 2022

Status

approved