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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.

%I A331327 #8 May 02 2021 12:04:52
%S A331327 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 A331327 1764,225,10,0,40320,13068,1624,85,1,0,362880,109584,13132,735,15,0,
%U A331327 3628800,1026576,118124,6769,175,1,0,39916800,10628640,1172700,67284,1960,21
%N A331327 T(n, k) = [x^k] Pochhammer(x, n-k) for n >= 0, 0 <= k <= floor(n/2). Irregular triangle read by rows.
%F A331327 Rows are the antidiagonals of A132393.
%e A331327 Triangle starts:
%e A331327 [ 0] 1;
%e A331327 [ 1] 0;
%e A331327 [ 2] 0, 1;
%e A331327 [ 3] 0, 1;
%e A331327 [ 4] 0, 2,     1;
%e A331327 [ 5] 0, 6,     3;
%e A331327 [ 6] 0, 24,    11,    1;
%e A331327 [ 7] 0, 120,   50,    6;
%e A331327 [ 8] 0, 720,   274,   35,   1;
%e A331327 [ 9] 0, 5040,  1764,  225,  10;
%e A331327 [10] 0, 40320, 13068, 1624, 85, 1;
%p A331327 A331327row := n -> seq(coeff(expand(pochhammer(x, n-k)), x, k), k=0..n/2):
%p A331327 seq(A331327row(n), n=0..13);
%t A331327 T[n_, k_] := Abs[StirlingS1[n - k, k]];
%t A331327 Table[T[n, k], {n, 0, 13}, {k, 0, Floor[n/2]}] // Flatten
%Y A331327 Row sums are: 1, 0, A237653.
%Y A331327 Cf. A132393.
%K A331327 nonn,tabf
%O A331327 0,8
%A A331327 _Peter Luschny_, Jan 25 2020