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A015357 Gaussian binomial coefficient [ n,8 ] for q=-3. 13
1, 4921, 36321901, 229798289941, 1526550040078063, 9974653139743515223, 65533580739687859229563, 429769342296322230713871283, 2820146424148466477944423359046, 18502040831058043147238631145734166 (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..200

Index entries for linear recurrences with constant coefficients, signature (4921,12105660,-8513737740,-2091825362718,169437854380158,4524549298283340,-42209826451809660,-112576695670863081,150094635296999121).

FORMULA

a(n) = Product_{i=1..8} ((-3)^(n-i+1)-1)/((-3)^i-1). - M. F. Hasler, Nov 03 2012

G.f.: -x^8 / ( (x-1)*(27*x+1)*(81*x-1)*(729*x-1)*(9*x-1)*(2187*x+1)*(3*x+1)*(6561*x-1)*(243*x+1) ). - R. J. Mathar, Sep 02 2016

MATHEMATICA

Table[QBinomial[n, 8, -3], {n, 8, 20}] (* Vincenzo Librandi, Nov 02 2012 *)

PROG

(Sage) [gaussian_binomial(n, 8, -3) for n in xrange(8, 18)] # Zerinvary Lajos, May 25 2009

(MAGMA) r:=8; q:=-3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 02 2012

(PARI) A015357(n, r=8, q=-3)=prod(i=1, r, (1-q^(n-i+1))/(1-q^i)) \\ M. F. Hasler, Nov 03 2012

CROSSREFS

Cf. Gaussian binomial coefficients [n,8] for q=-2..-13: A015356, A015359, A015360, A015361, A015363, A015364, A015365, A015367, A015368, A015369, A015370. - M. F. Hasler, Nov 03 2012

Sequence in context: A043480 A028550 A091878 * A241934 A185850 A260939

Adjacent sequences:  A015354 A015355 A015356 * A015358 A015359 A015360

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified March 26 14:18 EDT 2019. Contains 321497 sequences. (Running on oeis4.)