A215709 n-th derivative of (x^x)^((x^x)^x) at x=1.

1, 1, 4, 24, 172, 1420, 13968, 154336, 1914288, 26108208, 388596960, 6251899104, 108088087776, 1995840455232, 39183950494752, 814399382073120, 17856182764554240, 411671923447488768, 9952212794293198080, 251646630845685827328, 6640389412581544588800

Offset: 0

Author

Alois P. Heinz, Aug 21 2012

Keywords

• nonn

Comments

Also n-th derivative of (x^((x^x)^x))^x = x^(x^(x^2)*x) at x=1.

Links

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

Crossrefs

Column k=12 of A215703.

Cf. A005727, A179230, A179405, A215524.

Programs

Maple

a:= n-> n!*coeff(series(subs(x=x+1, x^(x^(x^2)*x) ), x, n+1), x, n):
seq(a(n), n=0..25);

Formula

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