A371995 - OEIS

%I #9 Apr 25 2024 13:23:09

%S 1,1,1,0,1,0,1,0,1,1,0,3,1,0,6,2,1,0,10,8,1,0,15,20,9,1,0,21,40,45,1,

%T 0,28,70,135,44,1,0,36,112,315,264,1,0,45,168,630,924,265,1,0,55,240,

%U 1134,2464,1855,1,0,66,330,1890,5544,7420,1854,1,0,78,440,2970,11088,22260,14832

%N Triangle read by rows: T(n, k) = binomial(n - k, k) * subfactorial(k), for n >= 0 and 0 <= k <= floor(n/2).

%F T(n, k) = A011973(n, k) * A000166(k).

%F The rows are the antidiagonals of A098825.

%e Triangle starts:

%e   [0] 1;

%e   [1] 1;

%e   [2] 1, 0;

%e   [3] 1, 0;

%e   [4] 1, 0,  1;

%e   [5] 1, 0,  3;

%e   [6] 1, 0,  6,  2;

%e   [7] 1, 0, 10,  8;

%e   [8] 1, 0, 15, 20,  9;

%e   [9] 1, 0, 21, 40, 45;

%t T[n_, k_] := Binomial[n - k, k] * Subfactorial[k];

%t Table[T[n, k], {n, 0, 9}, {k, 0, n/2}] // MatrixForm

%Y Cf. A000166, A011973, A098825, A372102 (row sums), A371998 (main diagonal).

%K nonn,tabf

%O 0,12

%A _Peter Luschny_, Apr 24 2024