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%I #5 Dec 08 2022 14:51:41
%S 1,1,2,4,12,12,36,132,180,120,576,2400,4080,3360,1680,14400,65760,
%T 126000,134400,75600,30240,518400,2540160,5382720,6350400,4838400,
%U 1995840,665280,25401600,131725440,299315520,396688320,325987200,190935360,60540480,17297280
%N Triangle read by rows. The coefficients of the polynomials hypergeom([-x, -x, -n], [-x - n, -x - n], 1) * Product_{j=1..n} (j + x)^2 in ascending order of powers.
%e Triangle T(n, k) starts:
%e [0] 1;
%e [1] 1, 2;
%e [2] 4, 12, 12;
%e [3] 36, 132, 180, 120;
%e [4] 576, 2400, 4080, 3360, 1680;
%e [5] 14400, 65760, 126000, 134400, 75600, 30240;
%e [6] 518400, 2540160, 5382720, 6350400, 4838400, 1995840, 665280;
%p p := (n,x) -> hypergeom([-x, -x, -n], [-x - n, -x - n], 1)*mul((j + x)^2, j=1..n): for n from 0 to 7 do seq(coeff(simplify(p(n,x)), x, k), k = 0..n) od;
%K nonn,tabl
%O 0,3
%A _Peter Luschny_, Nov 26 2022
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