A355007 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A355007

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

1

1, 0, 1, 0, 2, 4, 0, 6, 27, 27, 0, 24, 176, 384, 256, 0, 120, 1250, 4375, 6250, 3125, 0, 720, 9864, 48600, 110160, 116640, 46656, 0, 5040, 86436, 557032, 1764735, 2941225, 2470629, 823543, 0, 40320, 836352, 6723584, 27725824, 64225280, 84410368, 58720256, 16777216

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

OFFSET

0,5

LINKS

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

FORMULA

Sum_{k=0..n} (-1)^k * T(n,k) = A133942(n). - Alois P. Heinz, Mar 30 2023

Conjecture: T(n,k) = A056856(n,k)*n. - R. J. Mathar, Mar 31 2023

EXAMPLE

Table T(n, k) begins:

[0] 1;

[1] 0, 1;

[2] 0, 2, 4;

[3] 0, 6, 27, 27;

[4] 0, 24, 176, 384, 256;

[5] 0, 120, 1250, 4375, 6250, 3125;

[6] 0, 720, 9864, 48600, 110160, 116640, 46656;

[7] 0, 5040, 86436, 557032, 1764735, 2941225, 2470629, 823543;

MAPLE

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

MATHEMATICA

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

CROSSREFS

A000142 (column 1), A000407 (row sums), A000312 (main diagonal), A355006.

Sequence in context: A344031 A229534 A021810 * A073800 A076813 A049289

Adjacent sequences: A355004 A355005 A355006 * A355008 A355009 A355010

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Jun 17 2022

STATUS

approved