A215629 n-th derivative of x^(x^((x^x)^x)) at x=1.

1, 1, 2, 9, 80, 660, 6714, 77084, 1005640, 14572944, 233086920, 4066783512, 76906345944, 1566049091568, 34153725715368, 793996577407560, 19595885746343808, 511550462381982528, 14080034085212120256, 407434430977558009344, 12363449947108075756800

Offset: 0

Author

Alois P. Heinz, Aug 18 2012

Keywords

• nonn

Links

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

Crossrefs

Column k=16 of A215703.

Cf. A005727, A179230, A179405, A215522, A215524.

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..30);

Mathematica

m = 20;
CoefficientList[(x+1)^((x+1)^(((x+1)^(x+1))^(x+1))) + O[x]^(m+1), x]* Range[0, m]! (* Jean-François Alcover, Feb 07 2021 *)

Formula

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