A015293 Gaussian binomial coefficient [ n,4 ] for q = -7.

1, 2101, 5149551, 12328144851, 29612203932102, 71094673339606302, 170699761008128301202, 409849628721453245181802, 984049129188697468764456303, 2362701900656492615160524472603, 5672847283550509352791825564114953, 13620506320919298149305087013514770853

Offset: 4

Author

Olivier Gérard, Dec 11 1999

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 = 4..300
• Index entries for linear recurrences with constant coefficients, signature (2101, 735350, -36032150, -247180549, 282475249).

Programs

Magma

r:=4; q:=-7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 02 2016

Mathematica

QBinomial[Range[4,17],4,-7] (* Harvey P. Dale, Sep 24 2011 *)
Table[QBinomial[n, 4, -7], {n, 4, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

Sage

[gaussian_binomial(n,4,-7) for n in range(4,14)] # Zerinvary Lajos, May 27 2009

Extensions

More terms from Harvey P. Dale, Sep 24 2011