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.

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, 1854, 0, 924, 630, 630, 924, 0, 1854, 14833, 0, 7420, 4928, 5670, 4928, 7420, 0, 14833, 133496, 0, 66744, 44520, 49896, 49896, 44520, 66744, 0, 133496

Offset: 0

Author

Peter Luschny, Sep 05 2020

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0]      1;
[1]      0, 0;
[2]      1, 0,     1;
[3]      2, 0,     0,     2;
[4]      9, 0,     6,     0,     9;
[5]     44, 0,    20,    20,     0,    44;
[6]    265, 0,   135,    80,   135,     0,   265;
[7]   1854, 0,   924,   630,   630,   924,     0,  1854;
[8]  14833, 0,  7420,  4928,  5670,  4928,  7420,     0, 14833;
[9] 133496, 0, 66744, 44520, 49896, 49896, 44520, 66744,     0, 133496.
		

Crossrefs

Cf. A000166 (T(n,0) and T(n,n)), A087981 (row sums).

Programs

Maple

sf := n -> add((-1)^(n-j)*pochhammer(n-j+1, j), j=0..n):
T := (n, k) -> binomial(n,k)*sf(n-k)*sf(k):
seq(seq(T(n, k), k=0..n), n=0..9);