A331327 - OEIS

%I #8 May 02 2021 12:04:52

%S 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,

%T 1764,225,10,0,40320,13068,1624,85,1,0,362880,109584,13132,735,15,0,

%U 3628800,1026576,118124,6769,175,1,0,39916800,10628640,1172700,67284,1960,21

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

%F Rows are the antidiagonals of A132393.

%e Triangle starts:

%e [ 0] 1;

%e [ 1] 0;

%e [ 2] 0, 1;

%e [ 3] 0, 1;

%e [ 4] 0, 2,     1;

%e [ 5] 0, 6,     3;

%e [ 6] 0, 24,    11,    1;

%e [ 7] 0, 120,   50,    6;

%e [ 8] 0, 720,   274,   35,   1;

%e [ 9] 0, 5040,  1764,  225,  10;

%e [10] 0, 40320, 13068, 1624, 85, 1;

%p A331327row := n -> seq(coeff(expand(pochhammer(x, n-k)), x, k), k=0..n/2):

%p seq(A331327row(n), n=0..13);

%t T[n_, k_] := Abs[StirlingS1[n - k, k]];

%t Table[T[n, k], {n, 0, 13}, {k, 0, Floor[n/2]}] // Flatten

%Y Row sums are: 1, 0, A237653.

%Y Cf. A132393.

%K nonn,tabf

%O 0,8

%A _Peter Luschny_, Jan 25 2020