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A015398 Gaussian binomial coefficient [ n,10 ] for q=-10. 13
1, 9090909091, 91827364555463728191, 917356289265463645628926537191, 9174480340688613582018540679613398447191, 91743885968026547299515818524084563811678679347191, 917439777120042501293773510987809326410294679682025870347191 (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..110

FORMULA

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

MATHEMATICA

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

PROG

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

(MAGMA) r:=10; q:=-10; [&*[(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, A015392, A015393, A015394, A015397, A015399, A015401, A015402. - Vincenzo Librandi, Nov 04 2012

Sequence in context: A331412 A204407 A144651 * A034614 A140501 A216014

Adjacent sequences:  A015395 A015396 A015397 * A015399 A015400 A015401

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified February 22 12:33 EST 2020. Contains 332136 sequences. (Running on oeis4.)