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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
Eric Weisstein's World of Mathematics, Power Tower
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-François Alcover, May 31 2018, from Maple *)
CROSSREFS
Column k=5 of A295028.
Cf. A179505.
Sequence in context: A233083 A053984 A113181 * A295106 A295107 A295108
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 14 2017
STATUS
approved

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)