A179230 n-th derivative of x^(x^x) at x=1.

1, 1, 2, 9, 32, 180, 954, 6524, 45016, 360144, 3023640, 27617832, 271481880, 2775329232, 31188079272, 350827041000, 4441125248640, 54110311240512, 765546040603584, 9938498593229568, 156934910753107200, 2128783325724881280, 37775147271084647424

Offset: 0

Author

Henryk Trappmann (bo198214(AT)gmail.com), Jul 03 2010

Keywords

• sign

Comments

First term < 0: a(33) = -868875490363254484795699722301440.

Links

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

Crossrefs

Cf. A005727. Column k=4 of A215703. Column k=3 of A277537.

Cf. A295103.

Programs

Maple

a:= n-> n!*coeff(series(subs(x=x+1, x^(x^x) ), x, n+1), x, n):
seq(a(n), n=0..30);  # Alois P. Heinz, Aug 20 2012

Mathematica

Table[ D[ x^(x^x), {x, n}] /. x -> 1, {n, 0, 20}] (* Robert G. Wilson v, Jul 12 2010 *)
NestList[ Factor[ D[ #1, x]] &, x^x^x, 20] /. x -> 1 (* Robert G. Wilson v, Aug 10 2010 *)
Range[0, 22]! CoefficientList[ Series[(1 + x)^(1 + x)^(1 + x), {x, 0, 22}], x] (* Robert G. Wilson v, Feb 03 2013 *)

Formula

E.g.f.: (x+1)^((x+1)^(x+1)). - Alois P. Heinz, Aug 21 2012

Extensions

a(21)-a(22) from Alois P. Heinz, Aug 20 2012