A015303 Gaussian binomial coefficient [ n,4 ] for q = -13.

1, 26521, 761974851, 21752862899691, 621305270140974342, 17745052029585350965782, 506816536013640476467362442, 14475186854407942097510802411322

Offset

4,2

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 = 4..200

Index entries related to Gaussian binomial coefficients.

Index entries for linear recurrences with constant coefficients, signature (26521,58611410,-9905328290,-128011801489,137858491849).

Formula

a(n) = product_{i=1..4} ((-13)^(n-i+1)-1)/((-13)^i-1). - M. F. Hasler, Nov 03 2012

G.f.: -x^4 / ( (x-1)*(169*x-1)*(2197*x+1)*(13*x+1)*(28561*x-1) ). - R. J. Mathar, Aug 03 2016

Example

To illustrate the relation qC(n,r)=qC(n,n-r), here with r=4, n=r+1...r+3:
A015303(5) = 26521 = A015000(5),
A015303(6) = 761974851 = A015265(6),
A015303(7) = 21752862899691 = A015286(7).

Mathematica

Table[QBinomial[n, 4, -13], {n, 4, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Prog

(Sage) [gaussian_binomial(n, 4, -13) for n in range(4, 12)] # Zerinvary Lajos, May 27 2009
(PARI) A015303(n, r=4, q=-13)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012

Crossrefs

Cf. q-integers and Gaussian binomial coefficients [n,r] for q=-13: A015000, A015265 (r=2), A015286 (r=3), A015321 (r=5), A015337 (r=6), A015355 (r=7), A015370 (r=8), A015385 (r=9), A015402 (r=10), A015422 (r=11), A015438 (r=12). - M. F. Hasler, Nov 03 2012

Fifth row (r=4) or column (resp. diagonal) of A015129, read as square (resp. triangular) array.

Sequence in context: A275417 A206539 A273260 * A236622 A329785 A229592

Adjacent sequences: A015300 A015301 A015302 * A015304 A015305 A015306

Keyword

nonn,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved