A015370 -id:A015370 - cp's OEIS frontend

A015422 Gaussian binomial coefficient [ n,11 ] for q=-13.

1, -1664148937320, 3000174326048697741925710, -5374347381421937558314402513609688760, 9632029764916740618771445568833182996026908640493, -17262095767026556801586191040816999767731925288888540910160480

Offset: 11

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 = 11..90
Index entries related to Gaussian binomial coefficients.

Cf. Gaussian binomial coefficients [n,r] for q=-13: A015265 (r=2), A015286 (r=3), A015303 (r=4), A015321 (r=5), A015337 (r=6), A015355 (r=7), A015370 (r=8), A015385 (r=9), A015402 (r=10), A015438 (r=12). - M. F. Hasler, Nov 03 2012

r:=11; q:=-13; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 06 2012

Table[QBinomial[n, 11, -13], {n, 11, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

A015422(n,r=11,q=-13)=prod(i=1,r,(q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012

[gaussian_binomial(n,11,-13) for n in range(11,16)] # Zerinvary Lajos, May 28 2009

a(n) = Product_{i=1..11} ((-13)^(n-i+1)-1)/((-13)^i-1). - M. F. Hasler, Nov 03 2012

A015438 Gaussian binomial coefficient [ n,12 ] for q=-13.

Original entry on oeis.org

1, 21633936185161, 507029461102251552321630151, 11807441196984503845077844573952807835871, 275100402115798836253928241395289617394098490488956444, 6409295323626866454933457428954320223001885025904687118646704057084

Offset: 12

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 = 12..80
Index entries related to Gaussian binomial coefficients.

r:=12; q:=-13; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 06 2012

Table[QBinomial[n, 12, -13], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

A015438(n,r=12,q=-13)=prod(i=1,r,(q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012

[gaussian_binomial(n,12,-13) for n in range(12,17)] # Zerinvary Lajos, May 28 2009

a(n)=product_{i=1..12} ((-13)^(n-i+1)-1)/((-13)^i-1). - M. F. Hasler, Nov 03 2012

cp's OEIS Frontend

A015422 Gaussian binomial coefficient [ n,11 ] for q=-13.

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