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 A289541 #26 Jun 11 2025 10:27:30
%S A289541 1,1,2,8,37,187,1304,14606,222379,4141729,107836478,4466744372,
%T A289541 258501941713,18779494904263,1918824942497636,311738238353418074,
%U A289541 71234670515346760951,20564497734374127115501,8363824677163863282113162,5408580882753786431279731328
%N A289541 Number of subspaces of GF(2)^n with even dimension.
%H A289541 Vaclav Kotesovec, <a href="/A289541/b289541.txt">Table of n, a(n) for n = 0..100</a>
%F A289541 a(n)/[n]_q! is the coefficient of x^n in the expansion of exp_q(x)*cosh_q(x) when q->2, and cosh_q(x) = Sum_{n>=0} x^(2n)/[2n]_q!, and exp_q(x) is the q-exponential function, and [n]_q! is the q-factorial of n.
%F A289541 From _Vaclav Kotesovec_, Jun 11 2025: (Start)
%F A289541 a(n) ~ c * 2^(n^2/4), where
%F A289541 c = 3.89569562162... if mod(n,4) = 0,
%F A289541 c = 3.68597474538... if mod(n,4) = 1 or 3,
%F A289541 c = 3.47627317983... if mod(n,4) = 2. (End)
%t A289541 nn = 22; eq[z_] := Sum[z^n/FunctionExpand[QFactorial[n, q]], {n, 0, nn}];
%t A289541 coshq[z_] := Sum[z^(2 n)/FunctionExpand[QFactorial[(2 n), q]], {n, 0, nn}];
%t A289541 Table[FunctionExpand[QFactorial[n, q]] /. q -> 2, {n, 0, nn}]*
%t A289541 CoefficientList[Series[coshq[z]*eq[z] /. q -> 2, {z, 0, nn}], z]
%Y A289541 Cf. A182176, A289537, A289538, A289539, A289542.
%K A289541 nonn
%O A289541 0,3
%A A289541 _Geoffrey Critzer_, Jul 14 2017