A215522 n-th derivative of (x^x)^(x^x) at x=1.

1, 1, 4, 18, 100, 650, 4908, 41090, 382520, 3863808, 42409440, 497972112, 6259762320, 83343114504, 1175904241848, 17442325040520, 272149555445760, 4438451554802880, 75714874759039104, 1343817666163911168, 24837691533530152320, 475811860099666527360

Offset: 0

Author

Alois P. Heinz, Aug 14 2012

Keywords

• sign

Comments

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

First term < 0: a(65).

Links

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

Crossrefs

Column k=6 of A215703.

Cf. A005727, A179230, A179405, A215524.

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);

Mathematica

m = 21; CoefficientList[(x+1)^((x+1)^(x+2)) + O[x]^(m+1), x]*Range[0, m]! (* Jean-François Alcover, Feb 07 2021 *)

Formula

E.g.f.: (x+1)^((x+1)^(x+2)).