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A022215 Gaussian binomial coefficients [ n,8 ] for q = 5. 1
1, 488281, 198682027181, 78236053707784181, 30609934249224268600431, 11960833022875371081037525431, 4672499438759279108929231093087931, 1825218456001772231793929085435472462931, 712977784594148279816735342927316866304884806 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,2

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 = 8..190

FORMULA

G.f.: x^8/((1-x)*(1-5*x)*(1-25*x)*(1-125*x)*(1-625*x)*(1-3125*x)*(1-15625*x)*(1-78125*x)*(1-390625*x)). - Vincenzo Librandi, Aug 10 2016

a(n) = Product_{i=1..8} (5^(n-i+1)-1)/(5^i-1), by definition. - Vincenzo Librandi, Aug 10 2016

MATHEMATICA

Table[QBinomial[n, 8, 5], {n, 8, 20}] (* Vincenzo Librandi, Aug 10 2016 *)

PROG

(Sage) [gaussian_binomial(n, 8, 5) for n in xrange(8, 17)] # Zerinvary Lajos, May 25 2009

(MAGMA) r:=8; 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=8; q=5; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 08 2018

CROSSREFS

Sequence in context: A183695 A216070 A163401 * A252847 A251972 A034629

Adjacent sequences:  A022212 A022213 A022214 * A022216 A022217 A022218

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 23 05:36 EDT 2019. Contains 321422 sequences. (Running on oeis4.)