A215643 n-th derivative of x^((x^(x^x))^x) at x=1.

1, 1, 2, 15, 104, 890, 8814, 100660, 1288048, 18337680, 286674960, 4882660464, 89880715704, 1777384045944, 37552294300416, 843830334815640, 20086549955304384, 504750167170162944, 13348550475903813120, 370499740676381737728, 10766442934111876381440

Offset: 0

Author

Alois P. Heinz, Aug 18 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=15 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)).