A215705 n-th derivative of x^((x^x)^x) at x=1.

1, 1, 2, 15, 80, 590, 5034, 47110, 511216, 6019416, 77899320, 1092871824, 16459538952, 265695302808, 4560878625744, 83020743848760, 1595943389477760, 32291354360340672, 685838983512807360, 15248888357184824256, 354130117874225585280, 8571971677758345319680

Offset: 0

Author

Alois P. Heinz, Aug 21 2012

Keywords

• sign

Comments

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

First term < 0: a(272).

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300

Crossrefs

Column k=7 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..25);

Mathematica

With[{nn=30},CoefficientList[Series[(x+1)^((x+1)^((x+1)^2)),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Nov 30 2013 *)

Formula

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