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

0,5

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.

Formula

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

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 *)

Prog

(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))))};
for(n=0, 10, for(k=0, n, print1(T(n, k), ", "))) \\ G. C. Greubel, May 28 2018

Crossrefs

Sequence in context: A174097 A174040 A176078 * A015145 A040369 A040370

Adjacent sequences: A022179 A022180 A022181 * A022183 A022184 A022185

Keyword

nonn,tabl

Author

N. J. A. Sloane

Status

approved