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A371995
Triangle read by rows: T(n, k) = binomial(n - k, k) * subfactorial(k), for n >= 0 and 0 <= k <= floor(n/2).
1
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, 0, 28, 70, 135, 44, 1, 0, 36, 112, 315, 264, 1, 0, 45, 168, 630, 924, 265, 1, 0, 55, 240, 1134, 2464, 1855, 1, 0, 66, 330, 1890, 5544, 7420, 1854, 1, 0, 78, 440, 2970, 11088, 22260, 14832
OFFSET
0,12
FORMULA
T(n, k) = A011973(n, k) * A000166(k).
The rows are the antidiagonals of A098825.
EXAMPLE
Triangle starts:
[0] 1;
[1] 1;
[2] 1, 0;
[3] 1, 0;
[4] 1, 0, 1;
[5] 1, 0, 3;
[6] 1, 0, 6, 2;
[7] 1, 0, 10, 8;
[8] 1, 0, 15, 20, 9;
[9] 1, 0, 21, 40, 45;
MATHEMATICA
T[n_, k_] := Binomial[n - k, k] * Subfactorial[k];
Table[T[n, k], {n, 0, 9}, {k, 0, n/2}] // MatrixForm
CROSSREFS
Cf. A000166, A011973, A098825, A372102 (row sums), A371998 (main diagonal).
Sequence in context: A135670 A096754 A021767 * A071417 A096653 A308639
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, Apr 24 2024
STATUS
approved