login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A015363
Gaussian binomial coefficient [ n,8 ] for q=-7.
13
1, 5044201, 29684623509101, 170628488227082949701, 984049129188697468764456303, 5672509895284807570626050787828903, 32701168672146988445875611556849499108603, 188515500954498588979354521825234382842445990403
OFFSET
8,2
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
FORMULA
a(n) = Product_{i=1..8} ((-7)^(n-i+1)-1)/((-7)^i-1). - M. F. Hasler, Nov 03 2012
MATHEMATICA
QBinomial[Range[8, 20], 8, -7] (* Harvey P. Dale, May 09 2012 *)
Table[QBinomial[n, 8, -7], {n, 8, 19}] (* Vincenzo Librandi, Nov 03 2012 *)
PROG
(Sage) [gaussian_binomial(n, 8, -7) for n in range(8, 15)] # Zerinvary Lajos, May 25 2009
(Magma) r:=8; q:=-7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012
(PARI) A015363(n, r=8, q=-7)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012
CROSSREFS
Cf. Gaussian binomial coefficients [n,8] for q=-2..-13: A015356, A015357, A015359, A015360, A015361, A015364, A015365, A015367, A015368, A015369, A015370. - M. F. Hasler, Nov 03 2012
Sequence in context: A227155 A106785 A034607 * A234785 A206136 A186624
KEYWORD
nonn,easy
STATUS
approved