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 A022169 Triangle of Gaussian binomial coefficients [ n,k ] for q = 5. 20
 1, 1, 1, 1, 6, 1, 1, 31, 31, 1, 1, 156, 806, 156, 1, 1, 781, 20306, 20306, 781, 1, 1, 3906, 508431, 2558556, 508431, 3906, 1, 1, 19531, 12714681, 320327931, 320327931, 12714681, 19531, 1, 1, 97656, 317886556 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The coefficients of the matrix inverse are apparently given by T^(-1)(n,k) = (-1)^n*A157832(n,k). - R. J. Mathar, Mar 12 2013 REFERENCES F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698. M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351. LINKS G. C. Greubel, Rows n=0..50 of triangle, flattened R. Mestrovic, Lucas' theorem: its generalizations, extensions and applications (1878--2014), arXiv preprint 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. Index entries for sequences related to Gaussian binomial coefficients 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, 6, 1; 1, 31, 31, 1; 1, 156, 806, 156, 1; 1, 781, 20306, 20306, 781, 1; 1, 3906, 508431, 2558556, 508431, 3906, 1; 1, 19531, 12714681, 320327931, 320327931, 12714681, 19531, 1, MAPLE A027872 := proc(n) mul( 5^i-1, i=1..n) ; end proc: A022169 := proc(n, m) A027872(n)/A027872(n-m)/A027872(m) ; end proc: # R. J. Mathar, Mar 12 2013 MATHEMATICA p[n_] := Product[5^i-1, {i, 1, n}]; t[n_, k_] := p[n]/(p[k]*p[n-k]); Table[t[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 14 2014 *) Table[QBinomial[n, k, 5], {n, 0, 10}, {k, 0, n}]//Flatten (* or *) q:= 5; 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=5; T(n, k) = if(k==0, 1, if (k==n, 1, if (k<0 || n

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Last modified September 27 04:35 EDT 2023. Contains 365672 sequences. (Running on oeis4.)