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A015345 Gaussian binomial coefficient [ n,7 ] for q = -6. 2
1, -239945, 69088371619, -19251196169490725, 5393264335151280477835, -1509574711680960125598763925, 422593364163884169440003098013995, -118298673397216914972187267242547690325, 33116077152651051199781730118147946460139435 (list; graph; refs; listen; history; text; internal format)
OFFSET

7,2

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 = 7..190

Index entries for linear recurrences with constant coefficients, signature (-239945,11514768594,89124308917560,-115609163009731776,-24949102541146076160,902345215627683201024,5263661621405464657920,-6140942214464815497216)

FORMULA

G.f.: x^7 / ( (x-1)*(279936*x+1)*(216*x+1)*(36*x-1)*(7776*x+1)*(1296*x-1)*(6*x+1)*(46656*x-1) ). - R. J. Mathar, Sep 02 2016

MATHEMATICA

Table[QBinomial[n, 7, -6], {n, 7, 20}] (* Vincenzo Librandi, Nov 02 2012 *)

PROG

(Sage) [gaussian_binomial(n, 7, -6) for n in range(7, 15)] # Zerinvary Lajos, May 27 2009

(MAGMA) r:=7; q:=-6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..15]]; // Vincenzo Librandi, Nov 02 2012

CROSSREFS

Sequence in context: A237396 A234547 A234709 * A187960 A190388 A249194

Adjacent sequences:  A015342 A015343 A015344 * A015346 A015347 A015348

KEYWORD

sign,easy

AUTHOR

Olivier Gérard, Dec 11 1999

STATUS

approved

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Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)