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A295105 a(n) = (1/n) times the n-th derivative of the fifth tetration of x (power tower of order 5) x^^5 at x=1. 3
1, 1, 3, 14, 96, 729, 6842, 71861, 869936, 11639208, 172823592, 2797075786, 49197117648, 931938081060, 18931744650296, 410210251648404, 9443418462484224, 230108297407058144, 5915598580747789632, 159987606074180375904, 4539874767394840811904 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..434

Eric Weisstein's World of Mathematics, Power Tower

Wikipedia, Knuth's up-arrow notation

Wikipedia, Tetration

FORMULA

a(n) = 1/n * [(d/dx)^n x^^5]_{x=1}.

a(n) = (n-1)! * [x^n] (x+1)^^5.

a(n) = 1/n * A179505(n).

MAPLE

f:= proc(n) f(n):= `if`(n=0, 1, (x+1)^f(n-1)) end:

a:= n-> (n-1)!*coeff(series(f(5), x, n+1), x, n):

seq(a(n), n=1..23);

MATHEMATICA

f[n_] := f[n] = If[n == 0, 1, (x + 1)^f[n - 1]];

a[n_] := (n - 1)!*SeriesCoefficient[f[5], {x, 0, n}];

Array[a, 23] (* Jean-Fran├žois Alcover, May 31 2018, from Maple *)

CROSSREFS

Column k=5 of A295028.

Cf. A179505.

Sequence in context: A233083 A053984 A113181 * A295106 A295107 A295108

Adjacent sequences:  A295102 A295103 A295104 * A295106 A295107 A295108

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 14 2017

STATUS

approved

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Last modified August 3 17:26 EDT 2020. Contains 336200 sequences. (Running on oeis4.)