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A022196
Gaussian binomial coefficients [ n,5 ] for q = 3.
1
1, 364, 99463, 25095280, 6174066262, 1506472167928, 366573514642546, 89117945389585840, 21658948312410865183, 5263390747480701708292, 1279025522911365763892449, 310804949350361548416923680, 75525744222315755534269847164
OFFSET
5,2
FORMULA
G.f.: x^5/((1-x)*(1-3*x)*(1-9*x)*(1-27*x)*(1-81*x)*(1-243*x)). - Vincenzo Librandi, Aug 07 2016
a(n) = Product_{i=1..5} (3^(n-i+1)-1)/(3^i-1), by definition. - Vincenzo Librandi, Aug 06 2016
MATHEMATICA
Table[QBinomial[n, 5, 3], {n, 5, 20}] (* Vincenzo Librandi, Aug 07 2016 *)
PROG
(Sage) [gaussian_binomial(n, 5, 3) for n in range(5, 17)] # Zerinvary Lajos, May 25 2009
(Magma) r:=5; q:=3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 07 2016
(PARI) r=5; q=3; 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: A107509 A140935 A249671 * A098252 A221393 A099113
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Offset changed by Vincenzo Librandi, Aug 07 2016
STATUS
approved

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Last modified September 20 13:01 EDT 2024. Contains 376072 sequences. (Running on oeis4.)