A005168 n-th derivative of x^x at 1, divided by n. (Formerly M0380)

1, 1, 1, 2, 2, 9, -6, 118, -568, 4716, -38160, 358126, -3662088, 41073096, -500013528, 6573808200, -92840971200, 1402148010528, -22554146644416, 385014881294496, -6952611764874240, 132427188835260480, -2653529921603890560, 55802195178451990896

Offset

1,4

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..400 (first 100 terms from T. D. Noe)

R. K. Guy, Letter to N. J. A. Sloane, 1986

R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712.

R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712. [Annotated scanned copy]

R. R. Patterson and G. Suri, The derivatives of x^x, date unknown. Preprint. [Annotated scanned copy]

Maple

a:= n-> (n-1)! *coeftayl(x^x, x=1, n):
seq(a(n), n=1..30);  # Alois P. Heinz, Aug 18 2012

Mathematica

Rest[(NestList[ Factor[ D[ #1, x]] &, x^x, 23] /. (x -> 1))/Range[0, 23]] (* Robert G. Wilson v, Aug 10 2010 *)

Prog

(Python)
from sympy import var, diff
x = var('x')
y = x**x
l = [[y:=diff(y), y.subs(x, 1)/(n+1)][1] for n in range(10)]
print(l) # Nicholas Stefan Georgescu, Mar 02 2023

Crossrefs

Cf. A005727.

Column k=2 of A295027 (for n>1), A295028.

Sequence in context: A073315 A298597 A066320 * A256591 A011149 A212990

Adjacent sequences: A005165 A005166 A005167 * A005169 A005170 A005171

Keyword

sign,easy,nice

Author

N. J. A. Sloane, R. K. Guy

Extensions

One more term from Robert G. Wilson v, Aug 10 2010

Status

approved