A289383 revision #9
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A289383
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Total number of nonzero vectors over all subspaces of an n-dimensional vector space over the field with two elements.
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0
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0, 1, 6, 35, 240, 2077, 23562, 358775, 7449060, 213188689, 8473977534, 470309723435, 36582636406680, 3998655357260293, 615328930033081458, 133485330929459963615, 40859530900982506959180, 17659495180812130332490681, 10781678259164073608877557286, 9301770545157096607562560360595
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} A022166(n,k)*(2^k - 1).
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.
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MATHEMATICA
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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]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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editing
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