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A337615 T(n, k) = binomial(n, k)*sf(n-k)*sf(k) where sf is the subfactorial (A000166). Triangle read by rows, for 0 <= k <= n.

%I A337615 #5 Sep 05 2020 12:32:10
%S A337615 1,0,0,1,0,1,2,0,0,2,9,0,6,0,9,44,0,20,20,0,44,265,0,135,80,135,0,265,
%T A337615 1854,0,924,630,630,924,0,1854,14833,0,7420,4928,5670,4928,7420,0,
%U A337615 14833,133496,0,66744,44520,49896,49896,44520,66744,0,133496
%N A337615 T(n, k) = binomial(n, k)*sf(n-k)*sf(k) where sf is the subfactorial (A000166). Triangle read by rows, for 0 <= k <= n.
%e A337615 Triangle starts:
%e A337615 [0]      1;
%e A337615 [1]      0, 0;
%e A337615 [2]      1, 0,     1;
%e A337615 [3]      2, 0,     0,     2;
%e A337615 [4]      9, 0,     6,     0,     9;
%e A337615 [5]     44, 0,    20,    20,     0,    44;
%e A337615 [6]    265, 0,   135,    80,   135,     0,   265;
%e A337615 [7]   1854, 0,   924,   630,   630,   924,     0,  1854;
%e A337615 [8]  14833, 0,  7420,  4928,  5670,  4928,  7420,     0, 14833;
%e A337615 [9] 133496, 0, 66744, 44520, 49896, 49896, 44520, 66744,     0, 133496.
%p A337615 sf := n -> add((-1)^(n-j)*pochhammer(n-j+1, j), j=0..n):
%p A337615 T := (n, k) -> binomial(n,k)*sf(n-k)*sf(k):
%p A337615 seq(seq(T(n, k), k=0..n), n=0..9);
%Y A337615 Cf. A000166 (T(n,0) and T(n,n)), A087981 (row sums).
%K A337615 nonn,tabl
%O A337615 0,7
%A A337615 _Peter Luschny_, Sep 05 2020