A015368
Gaussian binomial coefficient [ n,8 ] for q=-11.
Original entry on oeis.org
1, 196495641, 42471590605551405, 9097327679593690752247605, 1950226184559914695131839252162415, 418045706884240723248900544124967821025015, 89611860518118688087749643530422009144522097477435
Offset: 8
- 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,8] for q=-2..-13:
A015356,
A015357,
A015359,
A015360,
A015361,
A015363,
A015364,
A015365,
A015367,
A015369,
A015370. -
M. F. Hasler, Nov 03 2012
-
r:=8; q:=-11; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012
-
Table[QBinomial[n, 8, -11], {n, 8, 14}] (* Vincenzo Librandi, Nov 03 2012 *)
-
A015368(n,r=8,q=-11)=prod(i=1,r,(q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012
-
[gaussian_binomial(n,8,-11) for n in range(8,14)] # Zerinvary Lajos, May 25 2009
A015369
Gaussian binomial coefficient [ n,8 ] for q=-12.
Original entry on oeis.org
1, 396906181, 171855836163195541, 73852125402551558141191381, 31756593605318274408653251348629973, 13654699102424414895934644240803700147539413, 5871272644707452307243912611380074655778555267227093
Offset: 8
- 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,8] for q=-2..-13:
A015356,
A015357,
A015359,
A015360,
A015361,
A015363,
A015364,
A015365,
A015367,
A015368,
A015370. -
M. F. Hasler, Nov 03 2012
-
r:=8; q:=-12; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012
-
A015369:=n->mul(((-12)^(n-i+1)-1)/((-12)^i-1), i=1..8): seq(A015369(n), n=8..20); # Wesley Ivan Hurt, Jan 29 2017
-
Table[QBinomial[n, 8, -12], {n, 8, 14}] (* Vincenzo Librandi, Nov 03 2012 *)
-
A015369(n,r=8,q=-12)=prod(i=1,r,(q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012
-
[gaussian_binomial(n,8,-12) for n in range(8,14)] # Zerinvary Lajos, May 24 2009