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A015375 Gaussian binomial coefficient [ n,9 ] for q=-3. 13
1, -14762, 326882347, -6204226946060, 123644349019377043, -2423717068608654822146, 47771556642163840723529281, -939857780045414554730512966640, 18502040831058043147238631145734166, -364157167636884405223950738210339855212 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,2

REFERENCES

J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.

M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 9..200

FORMULA

a(n) = Product_{i=1..9} ((-3)^(n-i+1)-1)/((-3)^i-1) (by definition). - Vincenzo Librandi, Nov 04 2012

G.f.: -x^9 / ( (x-1)*(27*x+1)*(81*x-1)*(729*x-1)*(9*x-1)*(2187*x+1)*(3*x+1)*(19683*x+1)*(6561*x-1)*(243*x+1) ). - R. J. Mathar, Sep 02 2016

MATHEMATICA

Table[QBinomial[n, 9, -3], {n, 9, 20}] (* Vincenzo Librandi, Nov 04 2012 *)

PROG

(Sage) [gaussian_binomial(n, 9, -3) for n in range(9, 18)] # Zerinvary Lajos, May 25 2009

(MAGMA) r:=9; q:=-3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 04 2012

CROSSREFS

Cf. Gaussian binomial coefficients [n,9] for q=-2..-13: A015371, A015376, A015377, A015378, A015379, A015380, A015381, A015382, A015383, A015384, A015385. - Vincenzo Librandi, Nov 04 2012

Sequence in context: A089315 A202314 A236667 * A043648 A272128 A035919

Adjacent sequences:  A015372 A015373 A015374 * A015376 A015377 A015378

KEYWORD

sign,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified February 22 04:55 EST 2020. Contains 332115 sequences. (Running on oeis4.)