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A015361 Gaussian binomial coefficient [ n,8 ] for q=-6. 13
1, 1439671, 2487182817955, 4158260859792814555, 6989674736616919292088715, 11738459947705882553575280369515, 19716527736890127515275338116221320235, 33116077152651051199781730118147946460139435, 55622326158904300663023790195853299389540017396395 (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..170

FORMULA

a(n) = Product_{i=1..8} ((-6)^(n-i+1)-1)/((-6)^i-1). - M. F. Hasler, Nov 03 2012

G.f.: -x^8 / ( (x-1)*(279936*x+1)*(216*x+1)*(36*x-1)*(7776*x+1)*(1296*x-1)*(6*x+1)*(46656*x-1)*(1679616*x-1) ). - R. J. Mathar, Sep 02 2016

MATHEMATICA

Table[QBinomial[n, 8, -6], {n, 8, 19}] (* Vincenzo Librandi, Nov 03 2012 *)

PROG

(Sage) [gaussian_binomial(n, 8, -6) for n in range(8, 15)] # Zerinvary Lajos, May 25 2009

(MAGMA) r:=8; q:=-6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012

(PARI) A015361(n, r=8, q=-6)=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, A015363, A015364, A015365, A015367, A015368, A015369, A015370. - M. F. Hasler, Nov 03 2012

Sequence in context: A204288 A321040 A234657 * A259306 A210629 A156621

Adjacent sequences:  A015358 A015359 A015360 * A015362 A015363 A015364

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified January 21 22:55 EST 2020. Contains 331129 sequences. (Running on oeis4.)