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A015397 Gaussian binomial coefficient [ n,10 ] for q=-9. 13
1, 3138105961, 11078672649879436966, 38576026619154398792076180886, 134526791875519431052113309866825757301, 469057975890128020293538941741406421614821552253, 1635507110993502253670495254060345828123783573932476807608 (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
FORMULA
a(n) = Product_{i=1..10} ((-9)^(n-i+1)-1)/((-9)^i-1) (by definition). - Vincenzo Librandi, Nov 04 2012
MATHEMATICA
Table[QBinomial[n, 10, -9], {n, 10, 20}] (* Vincenzo Librandi, Nov 04 2012 *)
PROG
(Sage) [gaussian_binomial(n, 10, -9) for n in range(10, 16)] # Zerinvary Lajos, May 25 2009
(Magma) r:=10; q:=-9; [&*[(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, A015398, A015399, A015401, A015402. - Vincenzo Librandi, Nov 04 2012
Sequence in context: A203886 A257914 A257893 * A291600 A092380 A096566
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified May 19 11:03 EDT 2024. Contains 372683 sequences. (Running on oeis4.)