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

0,8

Links

Table of n, a(n) for n=0..55.

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

Adjacent sequences: A331324 A331325 A331326 * A331328 A331329 A331330

Keyword

nonn,tabf

Author

Peter Luschny, Jan 25 2020

Status

approved