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 A015303 Gaussian binomial coefficient [ n,4 ] for q = -13. 12
 1, 26521, 761974851, 21752862899691, 621305270140974342, 17745052029585350965782, 506816536013640476467362442, 14475186854407942097510802411322 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,2 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 = 4..200 Index entries related to Gaussian binomial coefficients. Index entries for linear recurrences with constant coefficients, signature (26521,58611410,-9905328290,-128011801489,137858491849). FORMULA a(n) = product_{i=1..4} ((-13)^(n-i+1)-1)/((-13)^i-1). - M. F. Hasler, Nov 03 2012 G.f.: -x^4 / ( (x-1)*(169*x-1)*(2197*x+1)*(13*x+1)*(28561*x-1) ). - R. J. Mathar, Aug 03 2016 EXAMPLE To illustrate the relation qC(n,r)=qC(n,n-r), here with r=4, n=r+1...r+3: A015303(5) = 26521 = A015000(5), A015303(6) = 761974851 = A015265(6), A015303(7) = 21752862899691 = A015286(7). MATHEMATICA Table[QBinomial[n, 4, -13], {n, 4, 20}] (* Vincenzo Librandi, Oct 29 2012 *) PROG (Sage) [gaussian_binomial(n, 4, -13) for n in range(4, 12)] # Zerinvary Lajos, May 27 2009 (PARI) A015303(n, r=4, q=-13)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012 CROSSREFS Cf. q-integers and Gaussian binomial coefficients [n,r] for q=-13: A015000, A015265 (r=2), A015286 (r=3), A015321 (r=5), A015337 (r=6), A015355 (r=7), A015370 (r=8), A015385 (r=9), A015402 (r=10), A015422 (r=11), A015438 (r=12). - M. F. Hasler, Nov 03 2012 Fifth row (r=4) or column (resp. diagonal) of A015129, read as square (resp. triangular) array. Sequence in context: A275417 A206539 A273260 * A236622 A329785 A229592 Adjacent sequences: A015300 A015301 A015302 * A015304 A015305 A015306 KEYWORD nonn,easy AUTHOR Olivier Gérard, Dec 11 1999 STATUS approved

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Last modified September 12 07:48 EDT 2024. Contains 375843 sequences. (Running on oeis4.)