A289383 - OEIS

%I #16 Jul 15 2017 19:23:06

%S 0,1,6,35,240,2077,23562,358775,7449060,213188689,8473977534,

%T 470309723435,36582636406680,3998655357260293,615328930033081458,

%U 133485330929459963615,40859530900982506959180,17659495180812130332490681,10781678259164073608877557286,9301770545157096607562560360595

%N Total number of nonzero vectors over all subspaces of an n-dimensional vector space over the field with two elements.

%C The q-analog of A001787.

%F a(n) = Sum_{k=1..n} A022166(n,k)*(2^k - 1).

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

%F a(n) = (2^n - 1)*A006116(n-1).

%t 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[z eq[z]^2 /. q -> 2, {z, 0, nn}], z]

%Y Cf. A001787, A006116, A022166.

%K nonn

%O 0,3

%A _Geoffrey Critzer_, Jul 04 2017