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 A306895 Sum over all partitions of n of the power tower evaluation x^y^...^z, where x, y, ..., z are the parts in (weakly) increasing order. 5
 1, 1, 3, 5, 11, 18, 72, 387, 134349386, 115792089237316195423570985008687907853269984665640566457309223244801371506483 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(10) has 40403562 decimal digits. LINKS 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) = 1^1^1^1^1^1 + 1^1^1^1^2 + 1^1^2^2 + 2^2^2 + 1^1^1^3 + 1^2^3 + 3^3 + 1^1^4 + 2^4 + 1^5 + 6 = 1 + 1 + 1 + 16 + 1 + 1 + 27 + 1 + 16 + 1 + 6 = 72. MAPLE f:= l-> `if`(l=[], 1, l[1]^f(subsop(1=(), l))): a:= n-> add(f(sort(l, `<`)), l=combinat[partition](n)): seq(a(n), n=0..9); CROSSREFS Cf. A006906, A066186, A306884, A306901, A306902, A306903, A306919. Sequence in context: A162891 A320351 A319641 * A198519 A045957 A153065 Adjacent sequences:  A306892 A306893 A306894 * A306896 A306897 A306898 KEYWORD nonn AUTHOR Alois P. Heinz, Mar 15 2019 STATUS approved

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Last modified June 22 20:39 EDT 2021. Contains 345389 sequences. (Running on oeis4.)