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A022214
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Gaussian binomial coefficients [ n,7 ] for q = 5.
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1
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1, 97656, 7947261556, 625886840206056, 48975769621072897306, 3827456772141158994166056, 299039198587280398947721603556, 23362736428829868448189697999416056, 1825218456001772231793929085435472462931
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OFFSET
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7,2
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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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Vincenzo Librandi, Table of n, a(n) for n = 7..200
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FORMULA
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G.f.: x^7/((1-x)*(1-5*x)*(1-25*x)*(1-125*x)*(1-625*x)*(1-3125*x)*(1-15625*x)*(1-78125*x)). - Vincenzo Librandi, Aug 10 2016
a(n) = Product_{i=1..7} (5^(n-i+1)-1)/(5^i-1), by definition. - Vincenzo Librandi, Aug 10 2016
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MATHEMATICA
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Table[QBinomial[n, 7, 5], {n, 7, 20}] (* Harvey P. Dale, Sep 18 2011 *)
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PROG
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(Sage) [gaussian_binomial(n, 7, 5) for n in range(7, 16)] # Zerinvary Lajos, May 27 2009
(Magma) r:=7; q:=5; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 10 2016
(PARI) r=7; q=5; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 04 2018
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CROSSREFS
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Sequence in context: A184494 A251833 A145659 * A237509 A109185 A253823
Adjacent sequences: A022211 A022212 A022213 * A022215 A022216 A022217
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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