A350260 Triangle read by rows. T(n, k) = k^n * BellPolynomial(n, 1/k) for k > 0, if k = 0 then T(n, k) = k^n.

1, 0, 1, 0, 2, 3, 0, 5, 11, 19, 0, 15, 49, 109, 201, 0, 52, 257, 742, 1657, 3176, 0, 203, 1539, 5815, 15821, 35451, 69823, 0, 877, 10299, 51193, 170389, 447981, 1007407, 2026249, 0, 4140, 75905, 498118, 2032785, 6282416, 16157905, 36458010, 74565473

Offset: 0

Author

Peter Luschny, Dec 22 2021

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] 1
[1] 0,    1
[2] 0,    2,     3
[3] 0,    5,    11,     19
[4] 0,   15,    49,    109,     201
[5] 0,   52,   257,    742,    1657,    3176
[6] 0,  203,  1539,   5815,   15821,   35451,    69823
[7] 0,  877, 10299,  51193,  170389,  447981,  1007407,  2026249
[8] 0, 4140, 75905, 498118, 2032785, 6282416, 16157905, 36458010, 74565473
		

Crossrefs

Cf. A350256, A350257, A350258, A350259, A350261, A350262, A350263.

Cf. A000110, A301419.

Programs

Maple

A350260 := (n, k) -> ifelse(k = 0, k^n, k^n * BellB(n, 1/k)):
seq(seq(A350260(n, k), k = 0..n), n = 0..8);

Mathematica

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