A179405 n-th derivative of x^(x^(x^x)) at x=1.

1, 1, 2, 9, 56, 360, 2934, 26054, 269128, 3010680, 37616880, 504880992, 7387701672, 115228447152, 1929016301016, 34194883090440, 643667407174464, 12757366498618176, 266426229010029696, 5830527979298793024, 133665090871032478080, 3197905600674249843840

Offset: 0

Author

Robert G. Wilson v, Jul 13 2010

Keywords

• sign

Comments

First term < 0: a(329). - Alois P. Heinz, Sep 22 2015

Links

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

Crossrefs

Cf. A005727, A179230, A295104.

Column k=8 of A215703.

Column k=4 of A277537.

Programs

Maple

a:= n-> n!*coeff(series(subs(x=x+1, x^(x^(x^x)) ), x, n+1), x, n):
seq(a(n), n=0..30);  # Alois P. Heinz, Aug 20 2012

Mathematica

f[n_] := D[ x^(x^(x^x)), {x, n}] /. x -> 1; Array[f, 18, 0]
Range[0, 21]! CoefficientList[ Series[(1 + x)^(1 + x)^(1 + x)^(1 + x), {x, 0, 21}], x] (* Robert G. Wilson v, Feb 03 2013 *)

Formula

E.g.f.: (x+1)^((x+1)^((x+1)^(x+1))). - Alois P. Heinz, Aug 23 2012

Extensions

a(18)-a(21) from Alois P. Heinz, Aug 20 2012