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A306919
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Sum over all partitions of n into distinct parts of the power tower evaluation x^y^...^z, where x, y, ..., z are the parts in increasing order.
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3
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1, 1, 2, 4, 5, 14, 24, 122, 318, 2417851639229258349414245, 14134776518227074636666380005943348126619871175004951664972849610340964762
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OFFSET
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0,3
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LINKS
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EXAMPLE
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a(0) = 1 because the empty partition () has no parts, the exponentiation operator ^ is right-associative, and 1 is the right identity of exponentiation.
a(6) = 1^2^3 + 2^4 + 1^5 + 6 = 1 + 16 + 1 + 6 = 24.
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MAPLE
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d:= proc(l) local i; for i to nops(l)-1 do
if l[i]=l[i+1] then return fi od; l
end:
f:= l-> `if`(l=[], 1, l[1]^f(subsop(1=(), l))):
a:= n-> add(f(l), l=map(l->d(sort(l, `<`)), combinat[partition](n))):
seq(a(n), n=0..11);
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MATHEMATICA
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d[l_] := Module[{i}, For[i = 1, i <= Length[l]-1 , i++, If[l[[i]] == l[[i+1]], Return[]]]; l];
f[l_] := If[l == {}, 1, l[[1]]^f[Delete[l, 1]]];
a[n_] := Sum[f[l], {l, Sort /@ Select[IntegerPartitions[n], Length@# == Length @ Union@#&]}];
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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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approved
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