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.

1, 1, 3, 5, 11, 18, 72, 387, 134349386, 115792089237316195423570985008687907853269984665640566457309223244801371506483

Offset

0,3

Comments

a(10) has 40403562 decimal digits.

Links

Table of n, a(n) for n=0..9.

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 A364962

Adjacent sequences: A306892 A306893 A306894 * A306896 A306897 A306898

Keyword

nonn

Author

Alois P. Heinz, Mar 15 2019

Status

approved