A022184 Triangle of Gaussian binomial coefficients [ n,k ] for q = 20.

1, 1, 1, 1, 21, 1, 1, 421, 421, 1, 1, 8421, 168821, 8421, 1, 1, 168421, 67536821, 67536821, 168421, 1, 1, 3368421, 27014896821, 540362104821, 27014896821, 3368421, 1, 1, 67368421, 10805962096821, 4322923853464821

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=20. - G. C. Greubel, May 28 2018

Mathematica

Table[QBinomial[n, k, 20], {n, 0, 10}, {k, 0, n}]//Flatten (* or *) q:= 20; 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=20; 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

Row sums give A015211.

Sequence in context: A350999 A291073 A172301 * A176643 A015147 A174945

Adjacent sequences: A022181 A022182 A022183 * A022185 A022186 A022187

Keyword

nonn,tabl

Author

N. J. A. Sloane

Status

approved