A293844 Number of chains in the partially ordered (by subspace inclusion) set of all subspaces of the vector space GF(2)^n.
1, 3, 15, 143, 2783, 111231, 9031551, 1478288639, 485839107071, 319967908160511, 421866566365149183, 1112976522259306192895, 5873986737617632960438271, 62010172563368117470328995839, 1309330918812255261194272293584895, 55294146267102513780208470077042393087
Offset: 0
Keywords
Links
- Geoffrey Critzer, Combinatorics of Vector Spaces over Finite Fields, Master's thesis, Emporia State University, 2018.
Programs
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Mathematica
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]
Formula
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.