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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
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: A346355 A339477 A234657 * A259306 A210629 A156621
KEYWORD
nonn,easy
AUTHOR
_Olivier Gérard_
STATUS
approved

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Last modified February 29 23:21 EST 2024. Contains 370428 sequences. (Running on oeis4.)