A022188 Triangle of Gaussian binomial coefficients [ n,k ] for q = 24.

1, 1, 1, 1, 25, 1, 1, 601, 601, 1, 1, 14425, 346777, 14425, 1, 1, 346201, 199757977, 199757977, 346201, 1, 1, 8308825, 115060940953, 2761654032025, 115060940953, 8308825, 1, 1, 199411801, 66275110297753, 38177220399654553

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=24. - G. C. Greubel, May 30 2018

Mathematica

Table[QBinomial[n, k, 24], {n, 0, 10}, {k, 0, n}]//Flatten (* or *) q:= 24; 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 *)

Prog

(PARI) {q=24; 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 30 2018

Crossrefs

Row sums give A015217.

Sequence in context: A040625 A306454 A203550 * A040636 A040637 A040635

Adjacent sequences: A022185 A022186 A022187 * A022189 A022190 A022191

Keyword

nonn,tabl

Author

N. J. A. Sloane

Status

approved