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A022222
Gaussian binomial coefficients [ n,4 ] for q = 6.
1
1, 1555, 2072815, 2698853335, 3500412775495, 4537117983992551, 5880230843762528935, 7620806375898728694055, 9876570938882852540717095, 12800037205947411879866507815, 16588848493045381066264096333351
OFFSET
4,2
LINKS
FORMULA
G.f.: x^4/((1-x)*(1-6*x)*(1-36*x)*(1-216*x)*(1-1296*x)). - Vincenzo Librandi, Aug 11 2016
a(n) = Product_{i=1..4} (6^(n-i+1)-1)/(6^i-1), by definition. - Vincenzo Librandi, Aug 11 2016
MATHEMATICA
Table[QBinomial[n, 4, 6], {n, 4, 20}] (* Vincenzo Librandi, Aug 11 2016 *)
PROG
(Sage) [gaussian_binomial(n, 4, 6) for n in range(4, 15)] # Zerinvary Lajos, May 27 2009
(Magma) r:=4; q:=6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 11 2016
(PARI) r=4; q=6; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 07 2018
CROSSREFS
Sequence in context: A235306 A203501 A229434 * A166606 A252313 A252321
KEYWORD
nonn,easy
EXTENSIONS
Offset changed by Vincenzo Librandi, Aug 11 2016
STATUS
approved