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A015392 Gaussian binomial coefficient [ n,10 ] for q=-6. 13
1, 51828151, 3223388672928931, 194007802557550502202331, 11739968552378570066280405695371, 709779726467093092873777345973423761771, 42918585756017923252384776090351752769462732331 (list; graph; refs; listen; history; text; internal format)
OFFSET

10,2

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 = 10..140

FORMULA

a(n) = Product_{i=1..10} ((-6)^(n-i+1)-1)/((-6)^i-1) (by definition). - Vincenzo Librandi, Nov 04 2012

MATHEMATICA

Table[QBinomial[n, 10, -6], {n, 10, 20}] (* Vincenzo Librandi, Nov 04 2012 *)

PROG

(Sage) [gaussian_binomial(n, 10, -6) for n in xrange(10, 16)] # Zerinvary Lajos, May 25 2009

(MAGMA) r:=10; q:=-6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 04 2012

CROSSREFS

Cf. Gaussian binomial coefficients [n, 10] for q = -2..-13: A015386, A015388, A015390, A015391, A015393, A015394, A015397, A015398, A015399, A015401, A015402.

Sequence in context: A038829 A038818 A251497 * A211237 A105381 A004672

Adjacent sequences:  A015389 A015390 A015391 * A015393 A015394 A015395

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified March 26 06:48 EDT 2019. Contains 321481 sequences. (Running on oeis4.)