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A022173
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Triangle of Gaussian binomial coefficients [ n,k ] for q = 9.
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20
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1, 1, 1, 1, 10, 1, 1, 91, 91, 1, 1, 820, 7462, 820, 1, 1, 7381, 605242, 605242, 7381, 1, 1, 66430, 49031983, 441826660, 49031983, 66430, 1, 1, 597871, 3971657053, 322140667123, 322140667123, 3971657053
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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REFERENCES
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F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
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LINKS
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FORMULA
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EXAMPLE
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1 ;
1 1;
1 10 1;
1 91 91 1;
1 820 7462 820 1;
1 7381 605242 605242 7381 1;
1 66430 49031983 441826660 49031983 66430 1;
1 597871 3971657053 322140667123 322140667123 3971657053 597871 1;
1 5380840 321704819164 234844517989720 2113887057661126 234844517989720 321704819164 5380840 1 ;
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MAPLE
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mul(9^i-1, i=1..n) ;
end proc:
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MATHEMATICA
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a027878[n_]:=Times@@ Table[9^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, after Maple code *)
Table[QBinomial[n, k, 9], {n, 0, 10}, {k, 0, n}]//Flatten (* or *) q:= 9; 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 *)
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PROG
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(Python)
from operator import mul
def a027878(n): return 1 if n==0 else reduce(mul, [9**i - 1 for i in range(1, n + 1)])
def T(n, m): return a027878(n)/(a027878(m)*a027878(n - m))
for n in range(11): print([T(n, m) for m in range(n + 1)]) # Indranil Ghosh, Jul 20 2017, after Maple code
(PARI) {q=9; 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 27 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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