A350262 - OEIS

%I #8 Dec 30 2021 07:23:14

%S 1,-1,-1,-2,-1,0,-5,-1,1,1,21,25,19,9,1,1103,674,343,128,23,-2,29835,

%T 15211,6551,2133,379,-25,-9,739751,331827,123821,33479,3603,-1549,

%U -583,-9,16084810,5987745,1619108,120865,-174114,-112975,-32600,-3087,50

%N 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.

%e [0]        1

%e [1]       -1,      -1

%e [2]       -2,      -1,       0

%e [3]       -5,      -1,       1,      1

%e [4]       21,      25,      19,      9,       1

%e [5]     1103,     674,     343,    128,      23,      -2

%e [6]    29835,   15211,    6551,   2133,     379,     -25,     -9

%e [7]   739751,  331827,  123821,  33479,    3603,   -1549,   -583,    -9

%e [8] 16084810, 5987745, 1619108, 120865, -174114, -112975, -32600, -3087, 50

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

%p A350262 := (n, k) -> B(n, n - k + 1):

%p seq(seq(A350262(n, k), k = 0..n), n = 0..8);

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

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

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

%Y Cf. A000587, A009235.

%K sign,tabl

%O 0,4

%A _Peter Luschny_, Dec 22 2021