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A015365 Gaussian binomial coefficient [ n,8 ] for q=-9. 13
1, 38742049, 1688564650965445, 72587599955185580267365, 3125134483161392104770081009295, 134524513999723596604019036560420619887, 5790850118312580284352508983888376537699322083 (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} ((-9)^(n-i+1)-1)/((-9)^i-1). - M. F. Hasler, Nov 03 2012
MATHEMATICA
Table[QBinomial[n, 8, -9], {n, 8, 15}] (* Vincenzo Librandi, Nov 03 2012 *)
PROG
(Sage) [gaussian_binomial(n, 8, -9) for n in range(8, 14)] # Zerinvary Lajos, May 25 2009
(Magma) r:=8; q:=-9; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012
(PARI) A015365(n, r=8, q=-9)=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, A015361, A015363, A015364, A015367, A015368, A015369, A015370. - M. F. Hasler, Nov 03 2012
Sequence in context: A246232 A248710 A342350 * A272599 A105004 A216006
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified June 21 01:13 EDT 2024. Contains 373535 sequences. (Running on oeis4.)