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A022213 Gaussian binomial coefficients [ n,6 ] for q = 5. 1
1, 19531, 317886556, 5007031143556, 78360229974772306, 1224770494838892134806, 19138263752352528498478556, 299039198587280398947721603556, 4672499438759279108929231093087931, 73007841108236063781239140920167306681 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,2

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 = 6..200

FORMULA

G.f.: x^6/((1-x)*(1-5*x)*(1-25*x)*(1-125*x)*(1-625*x)*(1-3125*x)*(1-15625*x)). - Vincenzo Librandi, Aug 10 2016

a(n) = Product_{i=1..6} (5^(n-i+1)-1)/(5^i-1), by definition. - Vincenzo Librandi, Aug 10 2016

MATHEMATICA

Table[QBinomial[n, 6, 5], {n, 6, 20}] (* Vincenzo Librandi, Aug 10 2016 *)

PROG

(Sage) [gaussian_binomial(n, 6, 5) for n in xrange(6, 16)] # Zerinvary Lajos, May 27 2009

(MAGMA) r:=6; 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=6; 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: A206274 A033869 A031801 * A093219 A184493 A319062

Adjacent sequences:  A022210 A022211 A022212 * A022214 A022215 A022216

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Offset changed by Vincenzo Librandi, Aug 10 2016

STATUS

approved

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Last modified March 22 12:46 EDT 2019. Contains 321421 sequences. (Running on oeis4.)