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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

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

FORMULA

Rows are the antidigonals 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: A122930 A066387 A180663 * A301924 A262071 A011312

Adjacent sequences:  A331324 A331325 A331326 * A331328 A331329 A331330

KEYWORD

nonn,tabf

AUTHOR

Peter Luschny, Jan 25 2020

STATUS

approved

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Last modified March 28 17:51 EDT 2020. Contains 333103 sequences. (Running on oeis4.)