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A022183 Triangle of Gaussian binomial coefficients [ n,k ] for q = 19.

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%I A022183 #11 May 13 2019 08:49:24
%S A022183 1,1,1,1,20,1,1,381,381,1,1,7240,137922,7240,1,1,137561,49797082,
%T A022183 49797082,137561,1,1,2613660,17976884163,341607982520,17976884163,
%U A022183 2613660,1,1,49659541,6489657796503,2343107128988843
%N A022183 Triangle of Gaussian binomial coefficients [ n,k ] for q = 19.
%D A022183 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
%H A022183 G. C. Greubel, <a href="/A022183/b022183.txt">Rows n=0..50 of triangle, flattened</a>
%H A022183 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 A022183 T(n,k) = T(n-1,k-1) + q^k * T(n-1,k), with q=19. - _G. C. Greubel_, May 28 2018
%t A022183 Table[QBinomial[n,k,19], {n,0,10}, {k,0,n}]//Flatten (* or *) q:= 19; 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 A022183 (PARI) {q=19; 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 A022183 for(n=0,10, for(k=0,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, May 28 2018
%K A022183 nonn,tabl
%O A022183 0,5
%A A022183 _N. J. A. Sloane_