A015382
Gaussian binomial coefficient [ n,9 ] for q=-10.
Original entry on oeis.org
1, -909090909, 918273645463728191, -917356289173636281073462809, 917448033977125729275307703398447191, -917438859588520669588272049420660231320652809, 917439777028298615325746963688293507886210115870347191
Offset: 9
- 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.
Cf. Gaussian binomial coefficients [n, 9] for q = -2..-13:
A015371,
A015375,
A015376,
A015377,
A015378,
A015379,
A015380,
A015381,
A015383,
A015384,
A015385. -
Vincenzo Librandi, Nov 04 2012
-
r:=9; q:=-10; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 04 2012
-
Table[QBinomial[n, 9, -10],{n, 9, 20}] (* Vincenzo Librandi, Nov 04 2012 *)
A015383
Gaussian binomial coefficient [ n,9 ] for q=-11.
Original entry on oeis.org
1, -2161452050, 5139062461110267955, -12108543136400139930131294300, 28553261556033167915025118560778623715, -67326679110860591163925513616845073983121067050, 158752877164012182076561255078472431325233637546101158985
Offset: 9
- 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.
Cf. Gaussian binomial coefficients [n, 9] for q = -2..-13:
A015371,
A015375,
A015376,
A015377,
A015378,
A015379,
A015380,
A015381,
A015382,
A015384,
A015385. -
Vincenzo Librandi, Nov 04 2012
-
r:=9; q:=-11; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 04 2012
-
Table[QBinomial[n, 9, -11],{n, 9, 20}] (* Vincenzo Librandi, Nov 04 2012 *)
A015384
Gaussian binomial coefficient [ n,9 ] for q=-12.
Original entry on oeis.org
1, -4762874171, 24747240402737283733, -127616472670861852065241422635, 658504724872263265466971967899949697493, -3397726086395967282512946130260694347212577518123
Offset: 9
- 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.
Cf. Gaussian binomial coefficients [n, 9] for q = -2..-13:
A015371,
A015375,
A015376,
A015377,
A015378,
A015379,
A015380,
A015381,
A015382,
A015383,
A015385.
-
r:=9; q:=-12; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 04 2012
-
Table[QBinomial[n, 9, -12],{n, 9, 20}] (* Vincenzo Librandi, Nov 04 2012 *)