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A015438 Gaussian binomial coefficient [ n,12 ] for q=-13. 12
1, 21633936185161, 507029461102251552321630151, 11807441196984503845077844573952807835871, 275100402115798836253928241395289617394098490488956444, 6409295323626866454933457428954320223001885025904687118646704057084 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified April 15 11:27 EDT 2024. Contains 371681 sequences. (Running on oeis4.)