A015394 -id:A015394 - cp's OEIS frontend

A015401 Gaussian binomial coefficient [ n,10 ] for q=-12.

1, 57154490053, 3563602618051323347605, 220521264778812882986788501660885, 13654753975171772337501943609360145428875733, 845462977543736084817433183822531039414960234418458069

Offset: 10

Olivier Gérard

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.

Vincenzo Librandi, Table of n, a(n) for n = 10..100

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

a(n) = Product_{i=1..10} ((-12)^(n-i+1)-1)/((-12)^i-1) (by definition). - Vincenzo Librandi, Nov 05 2012

A015399 Gaussian binomial coefficient [ n,10 ] for q=-11.

Original entry on oeis.org

1, 23775972551, 621826557818118395106, 16116470915170412804822871108406, 418048302457998082359053173653182700919721, 10843028997901257369999365975865569183708813670389271

Offset: 10

Olivier Gérard

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.

Vincenzo Librandi, Table of n, a(n) for n = 10..100

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

a(n) = Product_{i=1..10} ((-11)^(n-i+1)-1)/((-11)^i-1) (by definition). - Vincenzo Librandi, Nov 05 2012

cp's OEIS Frontend

A015401 Gaussian binomial coefficient [ n,10 ] for q=-12.

Views

Author

Keywords

References

Links

Crossrefs

Programs

Magma

Mathematica

Sage

Formula