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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);

CROSSREFS

Cf. A022629, A066189, A306884, A306919.

Sequence in context: A168035 A247323 A099357 * A027038 A173929 A173299

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 July 15 16:09 EDT 2019. Contains 325049 sequences. (Running on oeis4.)