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%I #12 Jun 04 2019 02:58:31
%S 1,1,2,2,12,6,6,72,90,20,24,480,1080,560,70,120,3600,12600,11200,3150,
%T 252,720,30240,151200,201600,94500,16632,924,5040,282240,1905120,
%U 3528000,2425500,698544,84084,3432,40320,2903040,25401600,62092800,58212000,24216192,4708704,411840,12870
%N Triangle of coefficients of Bateman polynomial n!Z_n(-x).
%e {1};
%e {1, 2};
%e {2, 12, 6};
%e {6, 72, 90, 20};
%e {24, 480, 1080, 560, 70}; ...
%e 2!Z_2(-x) = 2+12x+6x^2.
%p A073768_row := proc(n) n!*hypergeom([-n, n+1], [1, 1], -x);
%p PolynomialTools:-CoefficientList(simplify(%), x) end:
%p seq(A073768_row(n), n=0..8): ListTools[FlattenOnce]([%]); # _Peter Luschny_, Jan 31 2016
%t T[n_, k_] := n! (n+k)! / (n-k)! / k!^3;
%t Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jun 04 2019 *)
%o (PARI) {T(n, k) = if( k<0 || k>n, 0, n! * (n+k)! / (n-k)! / k!^3)}
%Y A073767 gives row sums.
%K nonn,tabl
%O 0,3
%A _Michael Somos_, Aug 08 2002
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