A350259 Triangle read by rows. T(n, k) = n! * BellPolynomial(n, k).

1, 0, 1, 0, 4, 12, 0, 30, 132, 342, 0, 360, 2256, 7416, 18144, 0, 6240, 54480, 223920, 651360, 1545600, 0, 146160, 1749600, 8892720, 30496320, 82911600, 193030560, 0, 4420080, 71638560, 446357520, 1792405440, 5552593200, 14460979680, 33232948560

Offset: 0

Author

Peter Luschny, Dec 22 2021

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] 1
[1] 0,      1
[2] 0,      4,      12
[3] 0,     30,     132,     342
[4] 0,    360,    2256,    7416,    18144
[5] 0,   6240,   54480,  223920,   651360,  1545600
[6] 0, 146160, 1749600, 8892720, 30496320, 82911600, 193030560
		

Crossrefs

Cf. A350256, A350257, A350258, A350260, A350261, A350262, A350263.

Cf. A000110, A137341.

Programs

Maple

A350259 := (n, k) -> ifelse(n = 0, 1, n! * BellB(n, k)):
seq(seq(A350259(n, k), k = 0..n), n = 0..7);

Mathematica

T[n_, k_] := n! BellB[n, k]; Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten