Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 May 13 2019 08:49:17
%S 1,1,1,1,19,1,1,343,343,1,1,6175,111475,6175,1,1,111151,36124075,
%T 36124075,111151,1,1,2000719,11704311451,210711729475,11704311451,
%U 2000719,1,1,36012943,3792198910843,1228882510609651
%N Triangle of Gaussian binomial coefficients [ n,k ] for q = 18.
%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="/A022182/b022182.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=18. - _G. C. Greubel_, May 28 2018
%t 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 (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 for(n=0,10, for(k=0,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, May 28 2018
%K nonn,tabl
%O 0,5
%A _N. J. A. Sloane_