A350260 - OEIS

%I #8 Dec 30 2021 07:23:20

%S 1,0,1,0,2,3,0,5,11,19,0,15,49,109,201,0,52,257,742,1657,3176,0,203,

%T 1539,5815,15821,35451,69823,0,877,10299,51193,170389,447981,1007407,

%U 2026249,0,4140,75905,498118,2032785,6282416,16157905,36458010,74565473

%N 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.

%e Triangle starts:

%e [0] 1

%e [1] 0,    1

%e [2] 0,    2,     3

%e [3] 0,    5,    11,     19

%e [4] 0,   15,    49,    109,     201

%e [5] 0,   52,   257,    742,    1657,    3176

%e [6] 0,  203,  1539,   5815,   15821,   35451,    69823

%e [7] 0,  877, 10299,  51193,  170389,  447981,  1007407,  2026249

%e [8] 0, 4140, 75905, 498118, 2032785, 6282416, 16157905, 36458010, 74565473

%p A350260 := (n, k) -> ifelse(k = 0, k^n, k^n * BellB(n, 1/k)):

%p seq(seq(A350260(n, k), k = 0..n), n = 0..8);

%t T[n_, k_] := If[k == 0, k^n, k^n BellB[n, 1/k]];

%t Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten

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

%Y Cf. A000110, A301419.

%K nonn,tabl

%O 0,5

%A _Peter Luschny_, Dec 22 2021