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A022248 Gaussian binomial coefficients [ n,8 ] for q = 8. 1

%I

%S 1,19173961,326791806956681,5493386001237942388361,

%T 92186229916592298695053497993,1546675492323688689677277254864590473,

%U 25949007804224083420097621839124559742097033

%N Gaussian binomial coefficients [ n,8 ] for q = 8.

%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="/A022248/b022248.txt">Table of n, a(n) for n = 8..140</a>

%F a(n) = Product_{i=1..8} (8^(n-i+1)-1)/(8^i-1), by definition. - _Vincenzo Librandi_, Aug 06 2016

%F G.f.: x^8/((1 - x)*(1 - 8*x)*(1 - 64*x)*(1 - 512*x)*(1 - 4096*x)*(1 - 32768*x)*(1 - 262144*x)*(1 - 2097152*x)*(1 - 16777216*x)). - _Ilya Gutkovskiy_, Aug 06 2016

%t Table[QBinomial[n, 8, 8], {n, 8, 20}] (* _Vincenzo Librandi_, Aug 06 2016 *)

%o (Sage) [gaussian_binomial(n,8,8) for n in xrange(8,15)] # _Zerinvary Lajos_, May 25 2009

%o (MAGMA) r:=8; q:=8; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 06 2016

%K nonn,easy

%O 8,2

%A _N. J. A. Sloane_.

%E Offset changed by _Vincenzo Librandi_, Aug 06 2016

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Last modified April 25 12:19 EDT 2019. Contains 322456 sequences. (Running on oeis4.)