A295108 a(n) = (1/n) times the n-th derivative of the eighth tetration of x (power tower of order 8) x^^8 at x=1.

1, 1, 3, 14, 96, 849, 9362, 123101, 1847696, 31252368, 584145552, 11981318986, 267050704368, 6432872588700, 166461202886456, 4606491806670324, 135733988375074944, 4243153626928512224, 140252989224067186752, 4887395830953148166784, 179067423776388634331904

Offset: 1

Author

Alois P. Heinz, Nov 14 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..412
• Eric Weisstein's World of Mathematics, Power Tower
• Wikipedia, Knuth's up-arrow notation
• Wikipedia, Tetration

Crossrefs

Column k=8 of A295028.

Cf. A277539.

Programs

Maple

f:= proc(n) f(n):= `if`(n=0, 1, (x+1)^f(n-1)) end:
a:= n-> (n-1)!*coeff(series(f(8), 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[8], {x, 0, n}];
Array[a, 23] (* Jean-François Alcover, May 31 2018, from Maple *)

Formula

a(n) = 1/n * [(d/dx)^n x^^8]_{x=1}.

a(n) = (n-1)! * [x^n] (x+1)^^8.

a(n) = 1/n * A277539(n).