A350263 - OEIS

%I #4 Dec 23 2021 10:06:10

%S 1,0,-1,0,0,2,0,1,2,-3,0,1,-6,-21,-20,0,-2,-14,24,172,370,0,-9,26,195,

%T 108,-1105,-4074,0,-9,178,-111,-2388,-4805,2046,34293,0,50,90,-3072,

%U -3220,23670,87510,111860,-138312,0,267,-2382,-4053,47532,121995,-115458,-1193157,-2966088,-2932533

%N Triangle read by rows. T(n, k) = BellPolynomial(n, -k).

%e [0] 1

%e [1] 0,  -1

%e [2] 0,   0,     2

%e [3] 0,   1,     2,    -3

%e [4] 0,   1,    -6,   -21,   -20

%e [5] 0,  -2,   -14,    24,   172,    370

%e [6] 0,  -9,    26,   195,   108,  -1105, -  4074

%e [7] 0,  -9,   178,  -111, -2388,  -4805,    2046,    34293

%e [8] 0,  50,    90, -3072, -3220,  23670,   87510,   111860,  -138312

%e [9] 0, 267, -2382, -4053, 47532, 121995, -115458, -1193157, -2966088, -2932533

%p A350263 := (n, k) -> ifelse(n = 0, 1, BellB(n, -k)):

%p seq(seq(A350263(n, k), k = 0..n), n = 0..9);

%t T[n_, k_] := BellB[n, -k]; Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten

%Y Main diagonal: A292866, column 1: A000587, variant: A292861.

%K sign,tabl

%O 0,6

%A _Peter Luschny_, Dec 23 2021