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A022188 Triangle of Gaussian binomial coefficients [ n,k ] for q = 24.

%I A022188 #12 May 14 2019 14:59:37
%S A022188 1,1,1,1,25,1,1,601,601,1,1,14425,346777,14425,1,1,346201,199757977,
%T A022188 199757977,346201,1,1,8308825,115060940953,2761654032025,115060940953,
%U A022188 8308825,1,1,199411801,66275110297753,38177220399654553
%N A022188 Triangle of Gaussian binomial coefficients [ n,k ] for q = 24.
%D A022188 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
%H A022188 G. C. Greubel, <a href="/A022188/b022188.txt">Rows n=0..50 of triangle, flattened</a>
%H A022188 Kent E. Morrison, <a href="http://www.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 A022188 T(n,k) = T(n-1,k-1) + q^k * T(n-1,k), with q=24. - _G. C. Greubel_, May 30 2018
%t A022188 Table[QBinomial[n,k,24], {n,0,10}, {k,0,n}]//Flatten (* or *) q:= 24; 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 30 2018 *)
%o A022188 (PARI) {q=24; 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 A022188 for(n=0,10, for(k=0,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, May 30 2018
%Y A022188 Row sums give A015217.
%K A022188 nonn,tabl
%O A022188 0,5
%A A022188 _N. J. A. Sloane_