A215691 n-th derivative of (x^x)^(x^(x^x)) at x=1.

1, 1, 4, 18, 124, 950, 8688, 89600, 1038392, 13309272, 186471480, 2837173152, 46466835072, 815532508440, 15246845864040, 302533865599800, 6344720827608384, 140208886623418752, 3254819745378435264, 79172189409906466560, 2013138139856523598080

Offset: 0

Author

Alois P. Heinz, Aug 20 2012

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Column k=13 of A215703.

Cf. A005727, A179230, A179405, A215522, A215524, A215643.

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)+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)+1)).