A277539 n-th derivative of the eighth tetration of x (power tower of order 8) x^^8 at x=1.

1, 1, 2, 9, 56, 480, 5094, 65534, 984808, 16629264, 312523680, 6425601072, 143775827832, 3471659156784, 90060216241800, 2496918043296840, 73703868906725184, 2307477802376274048, 76376765284713220032, 2664806795257276548288, 97747916619062963335680

Offset: 0

Author

Alois P. Heinz, Oct 19 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400
• Eric Weisstein's World of Mathematics, Power Tower
• Wikipedia, Knuth's up-arrow notation
• Wikipedia, Tetration

Crossrefs

Column k=8 of A277537.

Cf. A215703, A295108.

Programs

Maple

f:= proc(n) f(n):= `if`(n=0, 1, (x+1)^f(n-1)) end:
a:= n-> n!*coeff(series(f(8), x, n+1), x, n):
seq(a(n), n=0..25);

Mathematica

f[n_] := f[n] = If[n == 0, 1, (x + 1)^f[n - 1]];
a[n_] := n!*SeriesCoefficient[f[8], {x, 0, n}];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, May 30 2018, from Maple *)

Formula

E.g.f.: (x+1)^^8.