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A015407 Gaussian binomial coefficient [ n,11 ] for q=-3. 2
1, -132860, 26477735830, -4522934399547980, 811239619864365082573, -143119691677080990521708240, 25388050075285266699527263288120, -4495361402895546052989488899628855120 (list; graph; refs; listen; history; text; internal format)
OFFSET

11,2

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 = 11..200

FORMULA

a(n) = Product_{i=1..11} ((-3)^(n-i+1)-1)/((-3)^i-1) (by definition). - Vincenzo Librandi, Nov 05 2012

MATHEMATICA

Table[QBinomial[n, 11, -3], {n, 11, 20}] (* Vincenzo Librandi, Nov 05 2012 *)

PROG

(Sage) [gaussian_binomial(n, 11, -3) for n in xrange(11, 19)] # Zerinvary Lajos, May 28 2009

(MAGMA) r:=11; q:=-3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 05 2012

CROSSREFS

Sequence in context: A238233 A242327 A319063 * A204536 A061732 A023046

Adjacent sequences:  A015404 A015405 A015406 * A015408 A015409 A015410

KEYWORD

sign,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified March 22 10:07 EDT 2019. Contains 321421 sequences. (Running on oeis4.)