The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A015306 Gaussian binomial coefficient [ n,5 ] for q = -3. 3
 1, -182, 49777, -11662040, 2869444942, -694405675964, 168973319623174, -41041673208656120, 9974653139743515223, -2423717068608654822146, 588973263031690760850991, -143119691677080990521708240 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,2 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 = 5..200 Index entries for linear recurrences with constant coefficients, signature (-182,16653,428220,-4046679,-10746918,14348907) FORMULA G.f.: x^5/((1-x)*(1+3*x)*(1-9*x)*(1+27*x)*(1-81*x)*(1+243*x)). - R. J. Mathar, Aug 03 2016 From G. C. Greubel, Sep 21 2019: (Start) a(n) = (1 - 61*(-3)^(n-4) + 610*(-3)^(2*n-7) - 610*(-3)^(3*n-9) + 61*(-3)^(4*n-10) - (-3)^(5*n-10))/17489920. E.g.f.: exp(-243*x)*(-1 +1830*exp(216*x) -44469*exp(240*x) +59049*exp(244 *x) -16470*exp(252*x) +61*exp(324*x))/1032762286080. (End) MAPLE seq((1 - 61*(-3)^(n-4) + 610*(-3)^(2*n-7) - 610*(-3)^(3*n-9) + 61*(-3)^(4*n-10) - (-3)^(5*n-10))/17489920, n=5..25); # G. C. Greubel, Sep 21 2019 MATHEMATICA Table[QBinomial[n, 5, -3], {n, 5, 20}] (* Vincenzo Librandi, Oct 29 2012 *) PROG (Sage) [gaussian_binomial(n, 5, -3) for n in range(5, 17)] # Zerinvary Lajos, May 27 2009 (PARI) a(n) = (1 - 61*(-3)^(n-4) + 610*(-3)^(2*n-7) - 610*(-3)^(3*n-9) + 61*(-3)^(4*n-10) - (-3)^(5*n-10))/17489920 \\ G. C. Greubel, Sep 21 2019 (Magma) [(1 - 61*(-3)^(n-4) + 610*(-3)^(2*n-7) - 610*(-3)^(3*n-9) + 61*(-3)^(4*n-10) - (-3)^(5*n-10))/17489920: n in [5..25]]; // G. C. Greubel, Sep 21 2019 (GAP) List([5..25], n-> (1 -61*(-3)^(n-4) +610*(-3)^(2*n-7) - 610*(-3)^(3*n-9) +61*(-3)^(4*n-10) -(-3)^(5*n-10))/17489920); # G. C. Greubel, Sep 21 2019 CROSSREFS Gaussian binomial coefficients [n,5]: A015305 (q=-2), this sequence (q=-3), A015308 (q=-4), A015309 (q=-5), A015310 (q=-6), A015312 (q=-7), A015313 (q=-8), A015315 (q=-9), A015316 (q=-10), A015317 (q=-11), A015319 (q=-12), A015321 (q=-13). Sequence in context: A048546 A225712 A371805 * A190830 A145525 A028676 Adjacent sequences: A015303 A015304 A015305 * A015307 A015308 A015309 KEYWORD sign,easy AUTHOR Olivier Gérard, Dec 11 1999 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 2 22:39 EDT 2024. Contains 374875 sequences. (Running on oeis4.)