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.

1, 1, 3, 14, 96, 729, 6842, 71861, 869936, 11639208, 172823592, 2797075786, 49197117648, 931938081060, 18931744650296, 410210251648404, 9443418462484224, 230108297407058144, 5915598580747789632, 159987606074180375904, 4539874767394840811904

Offset: 1

Author

Alois P. Heinz, Nov 14 2017

Keywords

• nonn

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

Crossrefs

Column k=5 of A295028.

Cf. A179505.

Programs

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 *)

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).