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A022232 Gaussian binomial coefficients [ n,3 ] for q = 7. 1
1, 400, 140050, 48177200, 16531644851, 5670690600800, 1945063360640100, 667157540444234400, 228835075951868449701, 78490432990886231801200, 26922218610904350161500150, 9234320988196680367732171600 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 3..200

FORMULA

G.f.: x^3/((1-x)*(1-7*x)*(1-49*x)*(1-343*x)).

a(n) = Product_{i=1..3} (7^(n-i+1)-1)/(7^i-1), by definition. - Vincenzo Librandi, Aug 06 2016

MATHEMATICA

Table[QBinomial[n, 3, 7], {n, 3, 20}] (* Vincenzo Librandi, Aug 06 2016 *)

PROG

(Sage) [gaussian_binomial(n, 3, 7) for n in xrange(3, 15)] # Zerinvary Lajos, May 27 2009

(MAGMA) r:=3; q:=7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 06 2016

(PARI) r=3; q=7; 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: A231288 A210262 A151608 * A151652 A197441 A268366

Adjacent sequences:  A022229 A022230 A022231 * A022233 A022234 A022235

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 24 19:48 EDT 2019. Contains 321448 sequences. (Running on oeis4.)