A022230 Gaussian binomial coefficients [ n,12 ] for q = 6.

1, 2612138803, 5848516394205967951, 12790160886494733304250601655, 27862895440026036935366271191556077095, 60659259454351187375733691191139808969963672263, 132044834674141024683472683631781840882298387938848321159

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..120

Formula

a(n) = Product_{i=1..12} (6^(n-i+1)-1)/(6^i-1), by definition. - Vincenzo Librandi, Aug 06 2016

G.f.: x^12/Product_{k=0..12} (1 - 6^k*x). - Ilya Gutkovskiy, Aug 06 2016

Mathematica

Table[QBinomial[n, 12, 6], {n, 12, 20}] (* Vincenzo Librandi, Aug 06 2016 *)

Prog

(Sage) [gaussian_binomial(n, 12, 6) for n in range(12, 19)] # Zerinvary Lajos, May 28 2009
(Magma) r:=12; q:=6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 06 2016
(PARI) r=12; q=6; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 13 2018

Crossrefs

Sequence in context: A288844 A028521 A064163 * A358483 A034648 A274816

Adjacent sequences: A022227 A022228 A022229 * A022231 A022232 A022233

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 06 2016

Status

approved