A015398
Gaussian binomial coefficient [ n,10 ] for q=-10.
Original entry on oeis.org
1, 9090909091, 91827364555463728191, 917356289265463645628926537191, 9174480340688613582018540679613398447191, 91743885968026547299515818524084563811678679347191, 917439777120042501293773510987809326410294679682025870347191
Offset: 10
- 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, 10] for q = -2..-13:
A015386,
A015388,
A015390,
A015391,
A015392,
A015393,
A015394,
A015397,
A015399,
A015401,
A015402. -
Vincenzo Librandi, Nov 04 2012
-
r:=10; q:=-10; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 04 2012
-
Table[QBinomial[n, 10, -10], {n, 10, 20}] (* Vincenzo Librandi, Nov 04 2012 *)
-
[gaussian_binomial(n,10,-10) for n in range(10,16)] # Zerinvary Lajos, May 25 2009
A015401
Gaussian binomial coefficient [ n,10 ] for q=-12.
Original entry on oeis.org
1, 57154490053, 3563602618051323347605, 220521264778812882986788501660885, 13654753975171772337501943609360145428875733, 845462977543736084817433183822531039414960234418458069
Offset: 10
- 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, 10] for q = -2..-13:
A015386,
A015388,
A015390,
A015391,
A015392,
A015393,
A015394,
A015397,
A015398,
A015399,
A015402.
-
r:=10; 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, 10, -12], {n, 10, 20}] (* Vincenzo Librandi, Nov 05 2012 *)
-
[gaussian_binomial(n,10,-12) for n in range(10,15)] # Zerinvary Lajos, May 25 2009
A015399
Gaussian binomial coefficient [ n,10 ] for q=-11.
Original entry on oeis.org
1, 23775972551, 621826557818118395106, 16116470915170412804822871108406, 418048302457998082359053173653182700919721, 10843028997901257369999365975865569183708813670389271
Offset: 10
- 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, 10] for q = -2..-13:
A015386,
A015388,
A015390,
A015391,
A015392,
A015393,
A015394,
A015397,
A015398,
A015401,
A015402.
-
r:=10; q:=-11; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 05 2012
-
Table[QBinomial[n, 10, -11], {n, 10, 20}] (* Vincenzo Librandi, Nov 05 2012 *)
-
[gaussian_binomial(n,10,-11) for n in range(10,16)] # Zerinvary Lajos, May 25 2009