A289539 Number of ways to choose a subspace U of GF(2)^n and then choose a subspace of U.

1, 3, 12, 66, 513, 5769, 95706, 2379348, 89759799, 5188919427, 463209471288, 64236626341974, 13903296824817117, 4713694025825766861, 2510421030027019810854, 2104931848782489253483752, 2783505220978001187684672531, 5813031971452642599096778614183

Offset: 0

Author

Geoffrey Critzer, Jul 12 2017

Keywords

• nonn

Comments

A q-analog (q=2) of A000244.

Crossrefs

Cf. A000244, A182176, A289537, A289538, A289541, A289542.

Programs

Mathematica

nn = 20; eq[z_] := Sum[z^n/FunctionExpand[QFactorial[n, q]], {n, 0, nn}];
Table[FunctionExpand[QFactorial[n, q]] /. q -> 2, {n, 0, nn}] CoefficientList[ Series[eq[z]^3 /. q -> 2, {z, 0, nn}], z]

Formula

a(n) = Sum_{k=0..n} A022166(n,k)*A006116(k).

a(n)/[n]_q! is the coefficient of x^n in the expansion of exp_q(x)^3 when q -> 2 and where exp_q(x) is the q-exponential function and [n]_q! is the q-factorial of n.