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 A306918 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 decreasing order. 2
 1, 1, 2, 5, 7, 18, 36, 118, 265, 263212, 2217881, 152599933940, 542101086242752217003726400434973829461152534, 63340828764059520458379290673240751904836319648345 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(14) = 620606987...270037949 has 183231 decimal digits. LINKS Table of n, a(n) for n=0..13. Eric Weisstein's World of Mathematics, Power Tower Wikipedia, Exponentiation Wikipedia, Identity element Wikipedia, Operator associativity Wikipedia, Partition (number theory) EXAMPLE 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) = 3^2^1 + 4^2 + 5^1 + 6 = 9 + 16 + 5 + 6 = 36. MAPLE 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..13); MATHEMATICA 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, ReverseSort /@ Select[IntegerPartitions[n], Length@# == Length@ Union@# &]}]; a /@ Range[0, 13] (* Jean-François Alcover, May 04 2020, after Maple *) CROSSREFS Cf. A022629, A066189, A306884, A306919. Sequence in context: A168035 A247323 A099357 * A027038 A341322 A173929 Adjacent sequences: A306915 A306916 A306917 * A306919 A306920 A306921 KEYWORD nonn AUTHOR Alois P. Heinz, Mar 16 2019 STATUS approved

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Last modified November 30 23:40 EST 2023. Contains 367464 sequences. (Running on oeis4.)