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A015424 Gaussian binomial coefficient [ n,12 ] for q=-3. 2
1, 398581, 238300021051, 122119467087816511, 65710531328480659504924, 34778150788062009177434607244, 18507923283033747485964552371646724, 9831373896055842251635498188040677794164 (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

Vincenzo Librandi, Table of n, a(n) for n = 12..180

FORMULA

a(n) = Product_{i=1..12} ((-3)^(n-i+1)-1)/((-3)^i-1) (by definition). - Vincenzo Librandi, Nov 06 2012

MATHEMATICA

QBinomial[Range[12, 20], 12, -3] (* Harvey P. Dale, Dec 18 2011 *)

Table[QBinomial[n, 12, -3], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

PROG

(Sage) [gaussian_binomial(n, 12, -3) for n in xrange(12, 20)] # Zerinvary Lajos, May 28 2009

(MAGMA) r:=12; q:=-3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 06 2012

CROSSREFS

Sequence in context: A250925 A230148 A209784 * A083634 A209910 A190837

Adjacent sequences:  A015421 A015422 A015423 * A015425 A015426 A015427

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified March 20 09:48 EDT 2019. Contains 321345 sequences. (Running on oeis4.)