A215706 n-th derivative of (((x^x)^x)^x)^x at x=1.

1, 1, 8, 48, 344, 3160, 31776, 349440, 4270304, 56343456, 794577600, 11975388480, 191431339392, 3225851451264, 57152333898240, 1061030230525440, 20569247105571840, 415385999498849280, 8719401647417757696, 189836589049809334272, 4278839631584572661760

Offset: 0

Author

Alois P. Heinz, Aug 21 2012

Keywords

• sign

Comments

Also n-th derivative of x^(x^4) at x=1.

First term < 0: a(130).

Links

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

Crossrefs

Column k=9 of A215703.

Cf. A005727, A179230, A179405, 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..25);

Formula

E.g.f.: (x+1)^((x+1)^4).