A215707 n-th derivative of ((x^x)^x)^(x^x) at x=1.

1, 1, 6, 33, 228, 1880, 17742, 187124, 2176360, 27617616, 378764280, 5574170712, 87491513304, 1457433784560, 25654258467432, 475431102931080, 9246150139382400, 188172595998890688, 3997389233216787264, 88440294467474068608, 2033755519425292281600

Offset: 0

Author

Alois P. Heinz, Aug 21 2012

Keywords

• sign

Comments

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

First term < 0: a(152).

Links

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

Crossrefs

Column k=10 of A215703.

Cf. A005727, A179230, A179405, A215524.

Programs

Maple

a:= n-> n!*coeff(series(subs(x=x+1, x^(x^x*x^2) ), x, n+1), x, n):
seq(a(n), n=0..25);

Formula

E.g.f.: (x+1)^((x+1)^(x+3)).