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A015365 Gaussian binomial coefficient [ n,8 ] for q=-9. 13
1, 38742049, 1688564650965445, 72587599955185580267365, 3125134483161392104770081009295, 134524513999723596604019036560420619887, 5790850118312580284352508983888376537699322083 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,2

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 = 8..140

FORMULA

a(n) = Product_{i=1..8} ((-9)^(n-i+1)-1)/((-9)^i-1). - M. F. Hasler, Nov 03 2012

MATHEMATICA

Table[QBinomial[n, 8, -9], {n, 8, 15}] (* Vincenzo Librandi, Nov 03 2012 *)

PROG

(Sage) [gaussian_binomial(n, 8, -9) for n in xrange(8, 14)] # Zerinvary Lajos, May 25 2009

(MAGMA) r:=8; q:=-9; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012

(PARI) A015365(n, r=8, q=-9)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012

CROSSREFS

Cf. Gaussian binomial coefficients [n,8] for q=-2..-13: A015356, A015357, A015359, A015360, A015361, A015363, A015364, A015367, A015368, A015369, A015370. - M. F. Hasler, Nov 03 2012

Sequence in context: A272517 A246232 A248710 * A272599 A105004 A216006

Adjacent sequences:  A015362 A015363 A015364 * A015366 A015367 A015368

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified March 19 04:34 EDT 2019. Contains 321311 sequences. (Running on oeis4.)