A215524 n-th derivative of (x^x)^x at x=1.

1, 1, 4, 12, 52, 240, 1188, 6804, 38960, 253296, 1654560, 11816640, 85816608, 668005728, 5240582592, 44667645120, 365989405440, 3494595006720, 28075694694912, 325862541872640, 2101211758356480, 39605981661066240, 48568198208302080, 7549838510211486720, -66667098077331572736

Offset: 0

Author

Alois P. Heinz, Aug 14 2012

Keywords

• sign

Links

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

Crossrefs

Column k=3 of A215703.

Cf. A005727, A179230, A179405, A215522.

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);

Mathematica

m = 24; CoefficientList[((x+1)^(x+1))^(x+1) + O[x]^(m+1), x]*Range[0, m]! (* Jean-François Alcover, Feb 07 2021 *)

Formula

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