A331327 T(n, k) = [x^k] Pochhammer(x, n-k) for n >= 0, 0 <= k <= floor(n/2). Irregular triangle read by rows.

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

Author

Peter Luschny, Jan 25 2020

Keywords

• nonn
• tabf

Examples

			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;
		

Crossrefs

Row sums are: 1, 0, A237653.

Cf. A132393.

Programs

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

Formula

Rows are the antidiagonals of A132393.