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%I #13 May 14 2019 12:23:55
%S 1,1,1,1,21,1,1,421,421,1,1,8421,168821,8421,1,1,168421,67536821,
%T 67536821,168421,1,1,3368421,27014896821,540362104821,27014896821,
%U 3368421,1,1,67368421,10805962096821,4322923853464821
%N Triangle of Gaussian binomial coefficients [ n,k ] for q = 20.
%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
%H G. C. Greubel, <a href="/A022184/b022184.txt">Rows n=0..50 of triangle, flattened</a>
%H Kent E. Morrison, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL9/Morrison/morrison37.html">Integer Sequences and Matrices Over Finite Fields</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
%F T(n,k) = T(n-1,k-1) + q^k * T(n-1,k), with q=20. - _G. C. Greubel_, May 28 2018
%t Table[QBinomial[n,k,20], {n,0,10}, {k,0,n}]//Flatten (* or *) q:= 20; T[n_, 0]:= 1; T[n_,n_]:= 1; T[n_,k_]:= T[n,k] = If[k < 0 || n < k, 0, T[n-1, k -1] +q^k*T[n-1,k]]; Table[T[n,k], {n,0,10}, {k,0,n}] // Flatten (* _G. C. Greubel_, May 28 2018 *)
%o (PARI) {q=20; T(n,k) = if(k==0,1, if (k==n, 1, if (k<0 || n<k, 0, T(n-1,k-1) + q^k*T(n-1,k))))};
%o for(n=0,10, for(k=0,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, May 28 2018
%Y Row sums give A015211.
%K nonn,tabl
%O 0,5
%A _N. J. A. Sloane_
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