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A022182 Triangle of Gaussian binomial coefficients [ n,k ] for q = 18.

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%I A022182 #11 May 13 2019 08:49:17
%S A022182 1,1,1,1,19,1,1,343,343,1,1,6175,111475,6175,1,1,111151,36124075,
%T A022182 36124075,111151,1,1,2000719,11704311451,210711729475,11704311451,
%U A022182 2000719,1,1,36012943,3792198910843,1228882510609651
%N A022182 Triangle of Gaussian binomial coefficients [ n,k ] for q = 18.
%D A022182 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
%H A022182 G. C. Greubel, <a href="/A022182/b022182.txt">Rows n=0..50 of triangle, flattened</a>
%H A022182 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 A022182 T(n,k) = T(n-1,k-1) + q^k * T(n-1,k), with q=18. - _G. C. Greubel_, May 28 2018
%t A022182 Table[QBinomial[n,k,18], {n,0,10}, {k,0,n}]//Flatten (* or *) q:= 18; 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 A022182 (PARI) {q=18; 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 A022182 for(n=0,10, for(k=0,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, May 28 2018
%K A022182 nonn,tabl
%O A022182 0,5
%A A022182 _N. J. A. Sloane_