A022205 Gaussian binomial coefficients [ n,6 ] for q = 4.

1, 5461, 23859109, 99277752549, 408235958349285, 1673768626404966885, 6857430062381149327845, 28089747579101385828291045, 115057361291389776393497498085, 471276749188750005563056686387685, 1930351405154232225472089767795511781

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)*(1-4*x)*(1-16*x)*(1-64*x)*(1-256*x)*(1-1024*x)*(1-4096*x)). - Vincenzo Librandi, Aug 11 2016

a(n) = Product_{i=1..6} (4^(n-i+1)-1)/(4^i-1), by definition. - Vincenzo Librandi, Aug 11 2016

Mathematica

Table[QBinomial[n, 6, 4], {n, 6, 20}] (* Vincenzo Librandi, Aug 11 2016 *)

Prog

(Sage) [gaussian_binomial(n, 6, 4) for n in range(6, 17)] # Zerinvary Lajos, May 27 2009
(Magma) r:=6; 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=6; q=4; 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: A028548 A069311 A258128 * A255193 A231269 A232037

Adjacent sequences: A022202 A022203 A022204 * A022206 A022207 A022208

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 11 2016

Status

approved