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A015432 Gaussian binomial coefficient [ n,12 ] for q=-9. 2
1, 254186582833, 72687171253825493271271, 20500882161928535478431441379312055, 5790937276726544621284284010937628428554805020, 1635504033452004972838895174119166771419593874338342173788, 461915515256190228639422934162753182948200513062452706826160310202324 (list; graph; refs; listen; history; text; internal format)
OFFSET
12,2
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..12} ((-9)^(n-i+1)-1)/((-9)^i-1) (by definition). - Vincenzo Librandi, Nov 06 2012
MATHEMATICA
Table[QBinomial[n, 12, -9], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)
PROG
(Sage) [gaussian_binomial(n, 12, -9) for n in range(12, 17)] # Zerinvary Lajos, May 28 2009
(Magma) r:=12; q:=-9; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 06 2012
CROSSREFS
Sequence in context: A076254 A213689 A348800 * A034618 A226858 A216904
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)