A015355 Gaussian binomial coefficient [ n,7 ] for q=-13.

1, -58266480, 3677897920745140, -230677643550873536294640, 14475186854407942097510802411322, -908294062111964496034866469968025332240

Offset

7,2

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 = 7..130

Index entries related to Gaussian binomial coefficients.

Formula

a(n) = Product_{i=1..7} ((-13)^(n-i+1)-1)/((-13)^i-1). - M. F. Hasler, Nov 03 2012

Mathematica

Table[QBinomial[n, 7, -13], {n, 7, 16}] (* Vincenzo Librandi, Nov 02 2012 *)

Prog

(Sage) [gaussian_binomial(n, 7, -13) for n in range(7, 13)] # Zerinvary Lajos, May 27 2009
(Magma) r:=7; q:=-13; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..15]]; // Vincenzo Librandi, Nov 02 2012
(PARI) A015355(n, r=7, q=-13)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 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), A015370 (r=8), A015385 (r=9), A015402 (r=10), A015422 (r=11), A015438 (r=12). - M. F. Hasler, Nov 03 2012

Sequence in context: A258422 A172679 A034612 * A321496 A320211 A320220

Adjacent sequences: A015352 A015353 A015354 * A015356 A015357 A015358

Keyword

sign,easy

Author

Olivier Gérard

Status

approved