A022195 Gaussian binomial coefficients [ n,12 ] for q = 2.

1, 8191, 44731051, 209386049731, 914807651274739, 3867895279362300499, 16094312257426532376339, 66441249531569955747981459, 273210326382611632738979052435, 1121258922081448861468067825426835, 4597164868683271949171164500871212435

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..200

Formula

a(n) = Product_{i=1..12} (2^(n-i+1)-1)/(2^i-1), by definition. - Vincenzo Librandi, Aug 03 2016

Mathematica

Table[QBinomial[n, 12, 2], {n, 12, 200}] (* Vincenzo Librandi, Aug 03 2016 *)

Prog

(Sage) [gaussian_binomial(n, 12, 2) for n in range(12, 23)] # Zerinvary Lajos, May 25 2009
(Magma) r:=12; q:=2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Aug 03 2016
(PARI) r=12; q=2; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, May 30 2018

Crossrefs

Sequence in context: A075956 A022529 A161024 * A069388 A069414 A289477

Adjacent sequences: A022192 A022193 A022194 * A022196 A022197 A022198

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 03 2016

Status

approved