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A022238 Gaussian binomial coefficients [ n,9 ] for q = 7. 1

%I

%S 1,47079208,1939395353553757,78490432990886231801200,

%T 3168691824510592423395247884703,

%U 127875753071992714335358328311551866824,5160291746051272234978893428859106387360586971,208236637980093164825596972398144064919402131047044800

%N Gaussian binomial coefficients [ n,9 ] for q = 7.

%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.

%H Vincenzo Librandi, <a href="/A022238/b022238.txt">Table of n, a(n) for n = 9..140</a>

%F G.f.: x^9/((1-x)*(1-7*x)*(1-49*x)*(1-343*x)*(1-2401*x)*(1-16807*x)*(1-117649*x)*(1-823543*x)*(1-5764801*x)*(1-40353607*x)). - _Vincenzo Librandi_, Aug 12 2016

%F a(n) = Product_{i=1..9} (7^(n-i+1)-1)/(7^i-1), by definition. - _Vincenzo Librandi_, Aug 12 2016

%t Table[QBinomial[n, 9, 7], {n, 9, 20}] (* _Vincenzo Librandi_, Aug 12 2016 *)

%o (Sage) [gaussian_binomial(n,9,7) for n in range(9,17)] # _Zerinvary Lajos_, May 25 2009

%o (MAGMA) r:=9; q:=7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 12 2016

%K nonn,easy

%O 9,2

%A _N. J. A. Sloane_

%E Offset changed by _Vincenzo Librandi_, Aug 12 2016

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Last modified October 26 18:30 EDT 2021. Contains 348268 sequences. (Running on oeis4.)