A015370 Gaussian binomial coefficient [ n,8 ] for q=-13.

1, 757464241, 621564749363392901, 506798783502833908602716981, 413425812255544017749839936272484623, 337243227617163445881817693983677965955870943, 275099718210633054941121644140453635236773122223471523

Offset: 8

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 = 8..100
• Index entries related to Gaussian binomial coefficients.

Crossrefs

Cf. Gaussian binomial coefficients [n,8] for q=-2..-12: A015356, A015357, A015359, A015360, A015361, A015363, A015364, A015365, A015367, A015368, A015369. - M. F. Hasler, Nov 03 2012

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), A015385 (r=9), A015402 (r=10), A015422 (r=11), A015438 (r=12). - M. F. Hasler, Nov 03 2012

Programs

Magma

r:=8; q:=-13; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012

Mathematica

Table[QBinomial[n, 8, -13], {n, 8, 14}] (* Vincenzo Librandi, Nov 03 2012 *)

PARI

A015370(n,r=8,q=-13)=prod(i=1,r,(q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012

Sage

[gaussian_binomial(n,8,-13) for n in range(8,14)] # Zerinvary Lajos, May 25 2009

Formula

a(n) = Product_{i=1..8} ((-13)^(n-i+1)-1)/((-13)^i-1). - M. F. Hasler, Nov 03 2012