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Triangle read by rows. T(n, k) = k^n * BellPolynomial(n, k).
6

%I #8 Dec 30 2021 07:23:30

%S 1,0,1,0,2,24,0,5,176,1539,0,15,1504,25029,193536,0,52,14528,453438,

%T 5558272,40250000,0,203,155520,9003879,173490176,1799296875,

%U 12508380288,0,877,1819392,193687281,5826740224,86070703125,803204128512,5430309951577

%N Triangle read by rows. T(n, k) = k^n * BellPolynomial(n, k).

%e Triangle starts:

%e [0] 1

%e [1] 0, 1

%e [2] 0, 2, 24

%e [3] 0, 5, 176, 1539

%e [4] 0, 15, 1504, 25029, 193536

%e [5] 0, 52, 14528, 453438, 5558272, 40250000

%e [6] 0, 203, 155520, 9003879, 173490176, 1799296875, 12508380288

%p A350257 := (n, k) -> ifelse(n = 0, 1, k^n * BellB(n, k)):

%p seq(seq(A350257(n, k), k = 0..n), n = 0..7);

%t T[n_, k_] := k^n BellB[n, k]; Table[T[n, k], {n, 0, 7}, {k, 0, n}] // Flatten

%Y Cf. A350256, A350258, A350259, A350260, A350261, A350262, A350263.

%Y Cf. A000110.

%K nonn,tabl

%O 0,5

%A _Peter Luschny_, Dec 22 2021