A022193 Gaussian binomial coefficients [n, 10] for q = 2.

1, 2047, 2794155, 3269560515, 3571013994483, 3774561792168531, 3926442969043883795, 4052305562169692070035, 4165817792093527797314451, 4274137206973266943778085267, 4380990637147598617372537398675

Offset

10,2

References

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.

Links

Vincenzo Librandi, Table of n, a(n) for n = 10..200

Formula

a(n) = Product_{i=1..10} (2^(n-i+1)-1)/(2^i-1), by definition. - Vincenzo Librandi, Aug 03 2016

G.f. assuming an offset of 0: exp( Sum_{n >= 1} b(11*n)/b(n)*x^n/n ) = 1 + 2047*x + 2794155*x^2 + ..., where b(n) = A000225(n) = 2^n - 1. - Peter Bala, Jul 03 2025

Mathematica

Table[QBinomial[n, 10, 2], {n, 10, 40}] (* Vincenzo Librandi, Aug 03 2016 *)

Prog

(SageMath) [gaussian_binomial(n, 10, 2) for n in range(10, 21)] # Zerinvary Lajos, May 25 2009
(Magma) r:=10; q:=2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 03 2016
(PARI) r=10; q=2; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, May 30 2018

Crossrefs

Gaussian binomial coefficient [n, k] for q = 2: A000225 (k = 1), A006095 (k = 2), A006096 (k = 3), A006097 (k = 4), A006110 (k = 5), A022189 - A022195 (k = 6 thru 12).

Sequence in context: A321550 A014233 A160964 * A069386 A069412 A069438

Adjacent sequences: A022190 A022191 A022192 * A022194 A022195 A022196

Keyword

nonn

Author

N. J. A. Sloane

Status

approved