|
|
A215522
|
|
n-th derivative of (x^x)^(x^x) at x=1.
|
|
7
|
|
|
1, 1, 4, 18, 100, 650, 4908, 41090, 382520, 3863808, 42409440, 497972112, 6259762320, 83343114504, 1175904241848, 17442325040520, 272149555445760, 4438451554802880, 75714874759039104, 1343817666163911168, 24837691533530152320, 475811860099666527360
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Also n-th derivative of (x^(x^x))^x = x^(x^x*x) at x=1.
First term < 0: a(65).
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: (x+1)^((x+1)^(x+2)).
|
|
MAPLE
|
a:= n-> n!*coeff(series(subs(x=x+1, (x^x)^(x^x) ), x, n+1), x, n):
seq(a(n), n=0..30);
|
|
MATHEMATICA
|
m = 21; CoefficientList[(x+1)^((x+1)^(x+2)) + O[x]^(m+1), x]*Range[0, m]! (* Jean-François Alcover, Feb 07 2021 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|