cp's OEIS Frontend

A371995 Triangle read by rows: T(n, k) = binomial(n - k, k) * subfactorial(k), for n >= 0 and 0 <= k <= floor(n/2).

%I A371995 #9 Apr 25 2024 13:23:09
%S A371995 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 A371995 0,28,70,135,44,1,0,36,112,315,264,1,0,45,168,630,924,265,1,0,55,240,
%U A371995 1134,2464,1855,1,0,66,330,1890,5544,7420,1854,1,0,78,440,2970,11088,22260,14832
%N A371995 Triangle read by rows: T(n, k) = binomial(n - k, k) * subfactorial(k), for n >= 0 and 0 <= k <= floor(n/2).
%F A371995 T(n, k) = A011973(n, k) * A000166(k).
%F A371995 The rows are the antidiagonals of A098825.
%e A371995 Triangle starts:
%e A371995   [0] 1;
%e A371995   [1] 1;
%e A371995   [2] 1, 0;
%e A371995   [3] 1, 0;
%e A371995   [4] 1, 0,  1;
%e A371995   [5] 1, 0,  3;
%e A371995   [6] 1, 0,  6,  2;
%e A371995   [7] 1, 0, 10,  8;
%e A371995   [8] 1, 0, 15, 20,  9;
%e A371995   [9] 1, 0, 21, 40, 45;
%t A371995 T[n_, k_] := Binomial[n - k, k] * Subfactorial[k];
%t A371995 Table[T[n, k], {n, 0, 9}, {k, 0, n/2}] // MatrixForm
%Y A371995 Cf. A000166, A011973, A098825, A372102 (row sums), A371998 (main diagonal).
%K A371995 nonn,tabf
%O A371995 0,12
%A A371995 _Peter Luschny_, Apr 24 2024