A289541 - OEIS

%I #21 Jul 17 2017 04:30:27

%S 1,1,2,8,37,187,1304,14606,222379,4141729,107836478,4466744372,

%T 258501941713,18779494904263,1918824942497636,311738238353418074,

%U 71234670515346760951,20564497734374127115501,8363824677163863282113162,5408580882753786431279731328

%N Number of subspaces of GF(2)^n with even dimension.

%F 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.

%t nn = 22; eq[z_] := Sum[z^n/FunctionExpand[QFactorial[n, q]], {n, 0, nn}];

%t coshq[z_] := Sum[z^(2 n)/FunctionExpand[QFactorial[(2 n), q]], {n, 0, nn}];

%t Table[FunctionExpand[QFactorial[n, q]] /. q -> 2, {n, 0, nn}]*

%t CoefficientList[Series[coshq[z]*eq[z] /. q -> 2, {z, 0, nn}], z]

%Y Cf. A182176, A289537, A289538, A289539, A289542.

%K nonn

%O 0,3

%A _Geoffrey Critzer_, Jul 14 2017