A350258 - OEIS

%I #8 Dec 30 2021 07:23:27

%S 1,0,1,0,2,12,0,5,44,342,0,15,188,1854,18144,0,52,908,11196,130272,

%T 1545600,0,203,4860,74106,1016544,13818600,193030560,0,877,28428,

%U 531378,8535264,132204600,2065854240,33232948560

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

%e Triangle starts:

%e [0] 1

%e [1] 0,   1

%e [2] 0,   2,    12

%e [3] 0,   5,    44,    342

%e [4] 0,  15,   188,   1854,   18144

%e [5] 0,  52,   908,  11196,  130272,   1545600

%e [6] 0, 203,  4860,  74106, 1016544,  13818600,  193030560

%e [7] 0, 877, 28428, 531378, 8535264, 132204600, 2065854240, 33232948560

%p A350258 := (n, k) -> ifelse(n = 0, 1, k! * BellB(n, k)):

%p seq(seq(A350258(n, k), k = 0..n), n = 0..7);

%t T[n_, k_] := k! BellB[n, k]; Table[T[n, k], {n, 0, 7}, {k, 0, n}] // Flatten

%Y Cf. A350256, A350257, A350259, A350260, A350261, A350262, A350263.

%Y Cf. A000110.

%K nonn,tabl

%O 0,5

%A _Peter Luschny_, Dec 22 2021