A015367
Gaussian binomial coefficient [ n,8 ] for q=-10.
Original entry on oeis.org
1, 90909091, 9182736463728191, 917356290091909926537191, 91744803489448201844894398447191, 9174388605059687035653977786959679347191, 917439777945737474914267633276565557306870347191
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,
A015368,
A015369,
A015370. -
M. F. Hasler, Nov 03 2012
-
r:=8; q:=-10; [&*[(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, -10], {n, 8, 14}] (* Vincenzo Librandi, Nov 03 2012 *)
-
A015367(n,r=8,q=-10)=prod(i=1,r,(q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012
-
[gaussian_binomial(n,8,-10) 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