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A015355
Gaussian binomial coefficient [ n,7 ] for q=-13.
12
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.
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
KEYWORD
sign,easy
STATUS
approved