A015402 Gaussian binomial coefficient [ n,10 ] for q=-13.

1, 128011456717, 17752510805031727164870, 2446220929187500105890055171302510, 337244135881870906696294510219932684378716373, 46491842741544248966048667175076748587505712393943779761

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..100

Index entries related to Gaussian binomial coefficients.

Formula

a(n) = Product_{i=1..10} ((-13)^(n-i+1)-1)/((-13)^i-1). - M. F. Hasler, Nov 03 2012

Mathematica

Table[QBinomial[n, 10, -13], {n, 10, 20}] (* Vincenzo Librandi, Nov 05 2012 *)

Prog

(Sage) [gaussian_binomial(n, 10, -13) for n in range(10, 15)] # Zerinvary Lajos, May 25 2009
(PARI) A015402(n, r=10, q=-13)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012
(Magma) r:=10; q:=-13; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 05 2012

Crossrefs

Cf. Gaussian binomial coefficients [n,r] for q=-13: A015265 (r=2), A015286 (r=3), A015303 (r=4), A015321 (r=5), A015337 (r=6), A015355 (r=7), A015370 (r=8), A015385 (r=9), A015422 (r=11), A015438 (r=12). - M. F. Hasler, Nov 03 2012

Cf. Gaussian binomial coefficients [n, 10] for q = -2..-13: A015386, A015388, A015390, A015391, A015392, A015393, A015394, A015397, A015398, A015399, A015401. - Vincenzo Librandi, Nov 05 2012

Sequence in context: A287238 A072718 A034652 * A108389 A172561 A172600

Adjacent sequences: A015399 A015400 A015401 * A015403 A015404 A015405

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved