A350257 Triangle read by rows. T(n, k) = k^n * BellPolynomial(n, k).

1, 0, 1, 0, 2, 24, 0, 5, 176, 1539, 0, 15, 1504, 25029, 193536, 0, 52, 14528, 453438, 5558272, 40250000, 0, 203, 155520, 9003879, 173490176, 1799296875, 12508380288, 0, 877, 1819392, 193687281, 5826740224, 86070703125, 803204128512, 5430309951577

Offset: 0

Author

Peter Luschny, Dec 22 2021

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] 1
[1] 0,   1
[2] 0,   2,      24
[3] 0,   5,     176,     1539
[4] 0,  15,    1504,    25029,     193536
[5] 0,  52,   14528,   453438,    5558272,    40250000
[6] 0, 203,  155520,  9003879,  173490176,  1799296875, 12508380288
		

Crossrefs

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

Cf. A000110.

Programs

Maple

A350257 := (n, k) -> ifelse(n = 0, 1, k^n * BellB(n, k)):
seq(seq(A350257(n, k), k = 0..n), n = 0..7);

Mathematica

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