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%I #17 Aug 02 2018 15:14:51
%S 1,3,15,143,2783,111231,9031551,1478288639,485839107071,
%T 319967908160511,421866566365149183,1112976522259306192895,
%U 5873986737617632960438271,62010172563368117470328995839,1309330918812255261194272293584895,55294146267102513780208470077042393087
%N Number of chains in the partially ordered (by subspace inclusion) set of all subspaces of the vector space GF(2)^n.
%H Geoffrey Critzer, <a href="https://esirc.emporia.edu/handle/123456789/3595">Combinatorics of Vector Spaces over Finite Fields</a>, Master's thesis, Emporia State University, 2018.
%F a(n)/A005329(n) is the coefficient of x^n in eq(x)^2/(2 - eq(x)) where eq(x) is the q-exponential function.
%t nn = 16; 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]^2/(1 - (eq[z] - 1)) /. q -> 2, {z, 0, nn}], z]
%Y Row sums of A293845.
%Y Cf. A005329, A289545.
%K nonn
%O 0,2
%A _Geoffrey Critzer_, Oct 17 2017
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