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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.
0
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
0,7
EXAMPLE
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.
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);
CROSSREFS
Cf. A000166 (T(n,0) and T(n,n)), A087981 (row sums).
Sequence in context: A165664 A019263 A244132 * A330607 A169776 A240766
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Sep 05 2020
STATUS
approved