A022208 Gaussian binomial coefficients [ n,9 ] for q = 4.

1, 349525, 97734250405, 26027119554103525, 6849609413493939400165, 1797339217481455290934231525, 471276749188750005563056686387685, 123549912998815788062283863044996567525

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..190

Formula

G.f.: x^9/((1-x)*(1-4*x)*(1-16*x)*(1-64*x)*(1-256*x)*(1-1024*x)*(1-4096*x)*(1-16384*x)*(1-65536*x)*(1-262144*x)). - Vincenzo Librandi, Aug 11 2016

a(n) = Product_{i=1..9} (4^(n-i+1)-1)/(4^i-1), by definition. - Vincenzo Librandi, Aug 11 2016

Mathematica

Table[QBinomial[n, 9, 4], {n, 9, 20}] (* Vincenzo Librandi, Aug 11 2016 *)

Prog

(Sage) [gaussian_binomial(n, 9, 4) for n in range(9, 17)] # Zerinvary Lajos, May 25 2009
(Magma) r:=9; q:=4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 11 2016
(PARI) r=9; q=4; 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: A166263 A338515 A069314 * A213018 A274245 A274254

Adjacent sequences: A022205 A022206 A022207 * A022209 A022210 A022211

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 11 2016

Status

approved