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A022230 Gaussian binomial coefficients [ n,12 ] for q = 6. 1
1, 2612138803, 5848516394205967951, 12790160886494733304250601655, 27862895440026036935366271191556077095, 60659259454351187375733691191139808969963672263, 132044834674141024683472683631781840882298387938848321159 (list; graph; refs; listen; history; text; internal format)
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 xrange(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 * A034648 A274816 A216902

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

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Last modified March 26 17:56 EDT 2019. Contains 321511 sequences. (Running on oeis4.)