A277541 n-th derivative of the tenth tetration of x (power tower of order 10) x^^10 at x=1.

1, 1, 2, 9, 56, 480, 5094, 65534, 984808, 16992144, 330667680, 7130797872, 168564160632, 4321664793264, 119356965323400, 3528831476247240, 111173720474673984, 3716755785886791168, 131414199676568655552, 4899052003032070987968, 192050612714621129114880

Offset: 0

Author

Alois P. Heinz, Oct 19 2016

Keywords

• nonn

Comments

Differs from A033917 first at n=11.

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=10 of A277537.

Cf. A033917, A215703, A295110.

Programs

Maple

f:= proc(n) f(n):= `if`(n=0, 1, (x+1)^f(n-1)) end:
a:= n-> n!*coeff(series(f(10), 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[10], {x, 0, n}];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, May 30 2018, from Maple *)

Formula

E.g.f.: (x+1)^^10.