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

1, 128011456717, 17752510805031727164870, 2446220929187500105890055171302510, 337244135881870906696294510219932684378716373, 46491842741544248966048667175076748587505712393943779761

Offset: 10

Author

Olivier Gérard

Keywords

• nonn
• easy

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.

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

Programs

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

Mathematica

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

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

Sage

[gaussian_binomial(n,10,-13) for n in range(10,15)] # Zerinvary Lajos, May 25 2009

Formula

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