A022210 Gaussian binomial coefficients [ n,11 ] for q = 4.

1, 5592405, 25019996065701, 106607206793565997285, 448896535558672700374937061, 1884649011792085827682980366254565, 7906721240160746987619507371870782509541, 33165216768196105736186294932151329554455695845

Offset

11,2

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 = 11..160

Formula

G.f.: x^11/((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)*(1-1048576*x)*(1-4194304*x)). - Vincenzo Librandi, Aug 11 2016

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

Mathematica

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

Prog

(Sage) [gaussian_binomial(n, 11, 4) for n in range(11, 19)] # Zerinvary Lajos, May 28 2009
(Magma) r:=11; 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=11; 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: A143686 A210011 A069316 * A057882 A379427 A210163

Adjacent sequences: A022207 A022208 A022209 * A022211 A022212 A022213

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 11 2016

Status

approved