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%I #7 Jul 29 2017 22:01:18
%S 1,0,1,1,281,9921,16078337,13596908545,191426147495937,
%T 3273234077014474753,497324772153177747947521,
%U 154709087482207635347155451905,291534668371237082293312814285062145,1534814232386517133354150755522868689240065,39269743760371912650589750432327799926355436503041,3338607968166762847572429548161284663670177988768356630529
%N Number of direct sum decompositions of GF(2)^n that do not contain any subspaces of dimension 1.
%C q-analog of A000296.
%H David Ellerman, <a href="http://arxiv.org/abs/1603.07619">The number of direct-sum decompositions of a finite vector space</a>, arXiv:1603.07619 [math.CO], 2016.
%H Kent E. Morrison, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Morrison/morrison37.html">Integer Sequences and Matrices Over Finite Fields</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1
%F a(n)/A002884(n) is the coefficient of x^n in the expansion of exp(Sum_{k>1}x^k/A002884(k)).
%t nn = 15; q := 2; g[n_] := (q - 1)^n q^Binomial[n, 2] FunctionExpand[QFactorial[n, q]]; G[z_] :=Sum[z^k/g[k], {k, 1, nn}];Table[g[n], {n, 0, nn}] CoefficientList[
%t Series[Exp[G[z] - z], {z, 0, nn}], z]
%Y Cf. A270881, A287406.
%K nonn
%O 0,5
%A _Geoffrey Critzer_, Jul 19 2017
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