A022191 Gaussian binomial coefficients [n, 8] for q = 2.

1, 511, 174251, 50955971, 13910980083, 3675639930963, 955841412523283, 246614610741341843, 63379954960524853651, 16256896431763117598611, 4165817792093527797314451, 1066968301301093995246996371, 273210326382611632738979052435

Offset

8,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 8..200

Formula

a(n) = Product_{i=1..8} (2^(n-i+1)-1)/(2^i-1), by definition. - Vincenzo Librandi, Aug 03 2016

G.f. with an offset of 0: exp( Sum_{n >= 1} b(9*n)/b(n)*x^n/n ) = 1 + 511*x +174251*x^2 + ..., where b(n) = A000225(n) = 2^n - 1. - Peter Bala, Jul 01 2025

Mathematica

Table[QBinomial[n, 8, 2], {n, 8, 40}] (* Vincenzo Librandi, Aug 03 2016 *)

Prog

(SageMath) [gaussian_binomial(n, 8, 2) for n in range(8, 20)] # Zerinvary Lajos, May 25 2009
(Magma) r:=8; 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=8; 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: A321554 A321548 A160956 * A069384 A069410 A289475

Adjacent sequences: A022188 A022189 A022190 * A022192 A022193 A022194

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 03 2016

Status

approved