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A022187 Triangle of Gaussian binomial coefficients [ n,k ] for q = 23.

%I A022187 #12 May 14 2019 16:13:45
%S A022187 1,1,1,1,24,1,1,553,553,1,1,12720,293090,12720,1,1,292561,155057330,
%T A022187 155057330,292561,1,1,6728904,82025620131,1886737591440,82025620131,
%U A022187 6728904,1,1,154764793,43391559778203,22956018300670611
%N A022187 Triangle of Gaussian binomial coefficients [ n,k ] for q = 23.
%D A022187 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
%H A022187 G. C. Greubel, <a href="/A022187/b022187.txt">rows n=0..50 of triangle, flattened</a>
%H A022187 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 A022187 T(n,k) = T(n-1,k-1) + q^k * T(n-1,k), with q=23. - _G. C. Greubel_, May 30 2018
%t A022187 Table[QBinomial[n,k,23], {n,0,10}, {k,0,n}]//Flatten (* or *) q:= 23; 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 A022187 (PARI) {q=23; 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 A022187 for(n=0,10, for(k=0,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, May 30 2018
%Y A022187 Row sums give A015215.
%K A022187 nonn,tabl
%O A022187 0,5
%A A022187 _N. J. A. Sloane_