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A331327
T(n, k) = [x^k] Pochhammer(x, n-k) for n >= 0, 0 <= k <= floor(n/2). Irregular triangle read by rows.
1
1, 0, 0, 1, 0, 1, 0, 2, 1, 0, 6, 3, 0, 24, 11, 1, 0, 120, 50, 6, 0, 720, 274, 35, 1, 0, 5040, 1764, 225, 10, 0, 40320, 13068, 1624, 85, 1, 0, 362880, 109584, 13132, 735, 15, 0, 3628800, 1026576, 118124, 6769, 175, 1, 0, 39916800, 10628640, 1172700, 67284, 1960, 21
OFFSET
0,8
FORMULA
Rows are the antidiagonals of A132393.
EXAMPLE
Triangle starts:
[ 0] 1;
[ 1] 0;
[ 2] 0, 1;
[ 3] 0, 1;
[ 4] 0, 2, 1;
[ 5] 0, 6, 3;
[ 6] 0, 24, 11, 1;
[ 7] 0, 120, 50, 6;
[ 8] 0, 720, 274, 35, 1;
[ 9] 0, 5040, 1764, 225, 10;
[10] 0, 40320, 13068, 1624, 85, 1;
MAPLE
A331327row := n -> seq(coeff(expand(pochhammer(x, n-k)), x, k), k=0..n/2):
seq(A331327row(n), n=0..13);
MATHEMATICA
T[n_, k_] := Abs[StirlingS1[n - k, k]];
Table[T[n, k], {n, 0, 13}, {k, 0, Floor[n/2]}] // Flatten
CROSSREFS
Row sums are: 1, 0, A237653.
Cf. A132393.
Sequence in context: A364518 A066387 A180663 * A301924 A262071 A011312
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, Jan 25 2020
STATUS
approved