A216351 n-th derivative of x^(x^(n-1)) at x=1.

1, 1, 2, 12, 156, 3160, 87990, 3218628, 150271520, 8710554816, 610951827960, 50770346742720, 4919197411068072, 548907184341479808, 69823173142960626480, 10034787531626188107840, 1616352219917942008147200, 289720383156740969786941440

Offset: 0

Author

Alois P. Heinz, Sep 04 2012

Keywords

• nonn

Comments

x^(x^(n-1)) = (((x^x)^x)^ ... )^x with n x's.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..275

Crossrefs

Cf. A000081, A216349, A216350, A215703.

Programs

Maple

a:= n-> n! *coeff(series( (x+1)^((x+1)^(n-1)) , x, n+1), x, n):
seq(a(n), n=0..20);

Formula

a(n) = n! * [x^n] (x+1)^((x+1)^(n-1)).

a(n) = A216349(n,1) = A216350(n,A000081(n)) for n>0.