A022214 Gaussian binomial coefficients [ n,7 ] for q = 5.

1, 97656, 7947261556, 625886840206056, 48975769621072897306, 3827456772141158994166056, 299039198587280398947721603556, 23362736428829868448189697999416056, 1825218456001772231793929085435472462931

Offset

7,2

References

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.

Links

Vincenzo Librandi, Table of n, a(n) for n = 7..200

Formula

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

Mathematica

Table[QBinomial[n, 7, 5], {n, 7, 20}] (* Harvey P. Dale, Sep 18 2011 *)

Prog

(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

Crossrefs

Sequence in context: A184494 A251833 A145659 * A237509 A109185 A253823

Adjacent sequences: A022211 A022212 A022213 * A022215 A022216 A022217

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved