A015438 Gaussian binomial coefficient [ n,12 ] for q=-13.

1, 21633936185161, 507029461102251552321630151, 11807441196984503845077844573952807835871, 275100402115798836253928241395289617394098490488956444, 6409295323626866454933457428954320223001885025904687118646704057084

Offset

12,2

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 = 12..80

Index entries related to Gaussian binomial coefficients.

Formula

a(n)=product_{i=1..12} ((-13)^(n-i+1)-1)/((-13)^i-1). - M. F. Hasler, Nov 03 2012

Mathematica

Table[QBinomial[n, 12, -13], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Prog

(Sage) [gaussian_binomial(n, 12, -13) for n in range(12, 17)] # Zerinvary Lajos, May 28 2009
(PARI) A015438(n, r=12, q=-13)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012
(Magma) r:=12; q:=-13; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 06 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), A015402 (r=10), A015422 (r=11). - M. F. Hasler, Nov 03 2012

Sequence in context: A172543 A298820 A246110 * A082249 A125735 A317777

Adjacent sequences: A015435 A015436 A015437 * A015439 A015440 A015441

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved