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 A022172 Triangle of Gaussian binomial coefficients [ n,k ] for q = 8. 15
 1, 1, 1, 1, 9, 1, 1, 73, 73, 1, 1, 585, 4745, 585, 1, 1, 4681, 304265, 304265, 4681, 1, 1, 37449, 19477641, 156087945, 19477641, 37449, 1, 1, 299593, 1246606473, 79936505481, 79936505481, 1246606473, 299593, 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 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. 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 9 1; 1 73 73 1; 1 585 4745 585 1; 1 4681 304265 304265 4681 1; 1 37449 19477641 156087945 19477641 37449 1; 1 299593 1246606473 79936505481 79936505481 1246606473 299593 1; 1 2396745 79783113865 40928737412745 327499862955657 40928737412745 79783113865 2396745 1 ; MAPLE A027876 := proc(n)     mul(8^i-1, i=1..n) ; end proc: A022172 := proc(n, m)     A027876(n)/A027876(m)/A027876(n-m) ; end proc: # R. J. Mathar, Jul 19 2017 MATHEMATICA a027878[n_]:=Times@@ Table[8^i - 1, {i, n}]; T[n_, m_]:=a027878[n]/( a027878[m] a027878[n - m]); Table[T[n, m], {n, 0, 10}, {m, 0, n}]//Flatten (* Indranil Ghosh, Jul 20 2017 *) Table[QBinomial[n, k, 8], {n, 0, 10}, {k, 0, n}]//Flatten (* or *) q:= 8; 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 (Python) from operator import mul def a027878(n): return 1 if n==0 else reduce(mul, [8**i - 1 for i in xrange(1, n + 1)]) def T(n, m): return a027878(n)/(a027878(m)*a027878(n - m)) for n in xrange(11): print [T(n, m) for m in xrange(n + 1)] # Indranil Ghosh, Jul 20 2017 (PARI) {q=8; T(n, k) = if(k==0, 1, if (k==n, 1, if (k<0 || n

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Last modified December 6 16:24 EST 2019. Contains 329808 sequences. (Running on oeis4.)