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 A022171 Triangle of Gaussian binomial coefficients [ n,k ] for q = 7. 16
 1, 1, 1, 1, 8, 1, 1, 57, 57, 1, 1, 400, 2850, 400, 1, 1, 2801, 140050, 140050, 2801, 1, 1, 19608, 6865251, 48177200, 6865251, 19608, 1, 1, 137257, 336416907, 16531644851, 16531644851, 336416907, 137257, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 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 R. Mestrovic, Lucas' theorem: its generalizations, extensions and applications (1878--2014),  arXiv:1409.3820 [math.NT], 2014. 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). - Peter A. Lawrence, Jul 13 2017 EXAMPLE 1 ; 1 1; 1 8 1; 1 57 57 1; 1 400 2850 400 1; 1 2801 140050 140050 2801 1; 1 19608 6865251 48177200 6865251 19608 1; 1 137257 336416907 16531644851 16531644851 336416907 137257 1; MAPLE A027875 := proc(n)     mul(7^i-1, i=1..n) ; end proc: A022171 := proc(n, m)     A027875(n)/A027875(m)/A027875(n-m) ; end proc: # R. J. Mathar, Jul 19 2017 MATHEMATICA p[n_]:=Product[7^i - 1, {i, 1, n}]; t[n_, k_]:=p[n]/(p[k]*p[n - k]); Table[t[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* Vincenzo Librandi, Aug 13 2016 *) Table[QBinomial[n, k, 7], {n, 0, 10}, {k, 0, n}]//Flatten (* or *) q:= 7; 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 27 2018 *) PROG (PARI) {q=7; T(n, k) = if(k==0, 1, if (k==n, 1, if (k<0 || n

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Last modified March 23 05:36 EDT 2019. Contains 321422 sequences. (Running on oeis4.)