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A371076 Triangle read by rows: T(n, k) = 3^n*Sum_{j=0..k} (-1)^(k - j)*binomial(k, j) * Pochhammer(j/3, n).

%I A371076 #10 Mar 13 2024 13:12:22
%S A371076 1,0,1,0,4,2,0,28,24,6,0,280,320,144,24,0,3640,5040,3120,960,120,0,
%T A371076 58240,92960,71280,30720,7200,720,0,1106560,1975680,1775760,960960,
%U A371076 319200,60480,5040,0,24344320,47653760,48545280,31127040,13104000,3548160,564480,40320
%N A371076 Triangle read by rows: T(n, k) = 3^n*Sum_{j=0..k} (-1)^(k - j)*binomial(k, j) * Pochhammer(j/3, n).
%F A371076 T(n, k) = k * T(n-1, k-1) + (3*n - 3 + k) * T(n-1, k) for 0 < k < n with initial values T(n, 0) = 0 for n > 0 and T(n, n) = n! for n >= 0. - _Werner Schulte_, Mar 13 2024
%e A371076 Triangle starts:
%e A371076 [0] 1;
%e A371076 [1] 0,       1;
%e A371076 [2] 0,       4,       2;
%e A371076 [3] 0,      28,      24,       6;
%e A371076 [4] 0,     280,     320,     144,     24;
%e A371076 [5] 0,    3640,    5040,    3120,    960,    120;
%e A371076 [6] 0,   58240,   92960,   71280,  30720,   7200,   720;
%e A371076 [7] 0, 1106560, 1975680, 1775760, 960960, 319200, 60480, 5040;
%p A371076 A371076 := (n, k) -> local j; 3^n*add((-1)^(k - j)*binomial(k, j)*pochhammer(j/3, n), j = 0..k): seq(seq(A371076(n, k), k = 0..n), n = 0..9);
%Y A371076 Cf. A371077, A007559 (column 1), A000142 (main diagonal), A052609 (subdiagonal).
%K A371076 nonn,tabl
%O A371076 0,5
%A A371076 _Peter Luschny_, Mar 10 2024