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A022200 Gaussian binomial coefficients [ n,9 ] for q = 3. 1
1, 29524, 653757313, 13362799477720, 266307564861468823, 5263390747480701708292, 103741619611085612124067759, 2042880353039758115797506899680, 40216143252770054194345243936096486, 791614563787525746761491781638123230424 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,2

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 = 9..200

FORMULA

G.f.: x^9/((1-x)*(1-3*x)*(1-9*x)*(1-27*x)*(1-81*x)*(1-243*x)*(1-729*x)*(1-2187*x)*(1-6561*x)*(1-19683*x)). - Vincenzo Librandi, Aug 10 2016

a(n) = Product_{i=1..9} (3^(n-i+1)-1)/(3^i-1), by definition. - Vincenzo Librandi, Aug 10 2016

MATHEMATICA

Table[QBinomial[n, 9, 3], {n, 9, 20}] (* Vincenzo Librandi, Aug 10 2016 *)

PROG

(Sage) [gaussian_binomial(n, 9, 3) for n in xrange(9, 19)] # Zerinvary Lajos, May 25 2009

(MAGMA)  r:=9; q:=3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 10 2016

(PARI) r=9; q=3; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 01 2018

CROSSREFS

Sequence in context: A182416 A232201 A251563 * A234669 A236734 A236317

Adjacent sequences:  A022197 A022198 A022199 * A022201 A022202 A022203

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Offset changed by Vincenzo Librandi, Aug 10 2016

STATUS

approved

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Last modified March 26 14:18 EDT 2019. Contains 321497 sequences. (Running on oeis4.)