A022211 Gaussian binomial coefficients [ n,12 ] for q = 4.

1, 22369621, 400319959420837, 6822861635108183247077, 114917519925881846404167134693, 1929880702992615813429218299211809253, 32385932129579122653905315624401024370889189

Offset

12,2

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 = 12..150

Formula

G.f.: x^12/((1-x)*(1-4*x)*(1-16*x)*(1-64*x)*(1-256*x)*(1-1024*x)*(1-4096*x)*(1-16384*x)*(1-65636*x)*(1-262144*x)*(1-1048576*x)*(1-4194304*x)*(1-16777216*x)). - Vincenzo Librandi, Aug 10 2016

a(n) = Product_{i=1..12} (4^(n-i+1)-1)/(4^i-1), by definition. - Vincenzo Librandi, Aug 10 2016

Mathematica

Table[QBinomial[n, 12, 4], {n, 12, 20}] (* Vincenzo Librandi, Aug 10 2016 *)

Prog

(Sage) [gaussian_binomial(n, 12, 4) for n in range(12, 19)] # Zerinvary Lajos, May 28 2009
(Magma) r:=12; q:=4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 10 2016
(PARI) r=12; 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: A112644 A179710 A069317 * A331358 A046397 A226479

Adjacent sequences: A022208 A022209 A022210 * A022212 A022213 A022214

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 10 2016

Status

approved