A289541 Number of subspaces of GF(2)^n with even dimension.

1, 1, 2, 8, 37, 187, 1304, 14606, 222379, 4141729, 107836478, 4466744372, 258501941713, 18779494904263, 1918824942497636, 311738238353418074, 71234670515346760951, 20564497734374127115501, 8363824677163863282113162, 5408580882753786431279731328

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

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.

Mathematica

nn = 22; eq[z_] := Sum[z^n/FunctionExpand[QFactorial[n, q]], {n, 0, nn}];
coshq[z_] := Sum[z^(2 n)/FunctionExpand[QFactorial[(2 n), q]], {n, 0, nn}];
Table[FunctionExpand[QFactorial[n, q]] /. q -> 2, {n, 0, nn}]*
CoefficientList[Series[coshq[z]*eq[z] /. q -> 2, {z, 0, nn}], z]

Crossrefs

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

Sequence in context: A361698 A305547 A007857 * A047729 A020076 A342052

Adjacent sequences: A289538 A289539 A289540 * A289542 A289543 A289544

Keyword

nonn

Author

Geoffrey Critzer, Jul 14 2017

Status

approved