A179505 n-th derivative of x^(x^(x^(x^x))) at x=1.

1, 1, 2, 9, 56, 480, 4374, 47894, 574888, 7829424, 116392080, 1901059512, 33564909432, 639562529424, 13047133134840, 283976169754440, 6563364026374464, 160538113862231808, 4141949353327046592, 112396373034208003008, 3199752121483607518080

Offset: 0

Author

Robert G. Wilson v, Jul 17 2010

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A005727, A179230, A179405, A295105.

Column k=17 of A215703.

Column k=5 of A277537.

Programs

Maple

a:= n-> n!*coeff(series(subs(x=x+1, x^(x^(x^(x^x))) ), x, n+1), x, n):
seq(a(n), n=0..25);  # Alois P. Heinz, Aug 21 2012

Mathematica

f[n_] := D[x^(x^(x^(x^x))), {x, n}] /. x -> 1; Array[f, 16, 0]
Range[0, 20]! CoefficientList[ Series[(1 + x)^(1 + x)^(1 + x)^(1 + x)^(1 + x), {x, 0, 20}], x] (* Robert G. Wilson v, Feb 03 2013 *)

Formula

E.g.f.: (x+1)^((x+1)^((x+1)^((x+1)^(x+1)))). - Alois P. Heinz, Aug 21 2012

Extensions

a(16)-a(20) from Alois P. Heinz, Aug 21 2012