A350262 Triangle read by rows. T(n, k) = B(n, n - k + 1) where B(n, k) = k^n * BellPolynomial(n, -1/k) for k > 0, if k = 0 then B(n, k) = k^n.

1, -1, -1, -2, -1, 0, -5, -1, 1, 1, 21, 25, 19, 9, 1, 1103, 674, 343, 128, 23, -2, 29835, 15211, 6551, 2133, 379, -25, -9, 739751, 331827, 123821, 33479, 3603, -1549, -583, -9, 16084810, 5987745, 1619108, 120865, -174114, -112975, -32600, -3087, 50

Offset: 0

Author

Peter Luschny, Dec 22 2021

Keywords

• sign
• tabl

Examples

			[0]        1
[1]       -1,      -1
[2]       -2,      -1,       0
[3]       -5,      -1,       1,      1
[4]       21,      25,      19,      9,       1
[5]     1103,     674,     343,    128,      23,      -2
[6]    29835,   15211,    6551,   2133,     379,     -25,     -9
[7]   739751,  331827,  123821,  33479,    3603,   -1549,   -583,    -9
[8] 16084810, 5987745, 1619108, 120865, -174114, -112975, -32600, -3087, 50
		

Crossrefs

Cf. A350256, A350257, A350258, A350259, A350260, A350261, A350263.

Cf. A000587, A009235.

Programs

Maple

B := (n, k) -> ifelse(k = 0, k^n, k^n * BellB(n, -1/k)):
A350262 := (n, k) -> B(n, n - k + 1):
seq(seq(A350262(n, k), k = 0..n), n = 0..8);

Mathematica

B[n_, k_] := If[k == 0, k^n, k^n BellB[n, -1/k]]; T[n_, k_] := B[n, n - k + 1];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten