This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A022191 #24 Jul 05 2025 05:20:52
%S A022191 1,511,174251,50955971,13910980083,3675639930963,955841412523283,
%T A022191 246614610741341843,63379954960524853651,16256896431763117598611,
%U A022191 4165817792093527797314451,1066968301301093995246996371,273210326382611632738979052435
%N A022191 Gaussian binomial coefficients [n, 8] for q = 2.
%H A022191 Vincenzo Librandi, <a href="/A022191/b022191.txt">Table of n, a(n) for n = 8..200</a>
%F A022191 a(n) = Product_{i=1..8} (2^(n-i+1)-1)/(2^i-1), by definition. - _Vincenzo Librandi_, Aug 03 2016
%F A022191 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
%t A022191 Table[QBinomial[n, 8, 2], {n, 8, 40}] (* _Vincenzo Librandi_, Aug 03 2016 *)
%o A022191 (Sage) [gaussian_binomial(n,8,2) for n in range(8,20)] # _Zerinvary Lajos_, May 25 2009
%o A022191 (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
%o A022191 (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
%Y A022191 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).
%K A022191 nonn
%O A022191 8,2
%A A022191 _N. J. A. Sloane_
%E A022191 Offset changed by _Vincenzo Librandi_, Aug 03 2016