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

1, 1, 1, 1, 19, 1, 1, 343, 343, 1, 1, 6175, 111475, 6175, 1, 1, 111151, 36124075, 36124075, 111151, 1, 1, 2000719, 11704311451, 210711729475, 11704311451, 2000719, 1, 1, 36012943, 3792198910843, 1228882510609651

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• tabl

References

• F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.

Links

• G. C. Greubel, Rows n=0..50 of triangle, flattened
• Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

Programs

Mathematica

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 *)

PARI

{q=18; T(n,k) = if(k==0,1, if (k==n, 1, if (k<0 || nG. C. Greubel, May 28 2018

Formula

T(n,k) = T(n-1,k-1) + q^k * T(n-1,k), with q=18. - G. C. Greubel, May 28 2018