A215265 (n-1)^(n+1) - n^n.

-2, -1, -3, -11, -13, 971, 31469, 856073, 23576391, 686321335, 21381059609, 714688329389, 25606611695675, 981043357956611, 40073886188532741, 1740059447428511761, 80079381261983807759, 3895126220983308449519, 199726027609854787271729

Offset

0,1

Comments

0^0 is interpreted as 1.

Links

Table of n, a(n) for n=0..18.

Formula

For n>0, a(n) = A046065(n-1) - A101334(n).

E.g.f.: x/W(-x) - (1+x)/(1+W(-x)) - x/(1+W(-x))^2 + x/(1+W(-x))^3, where W is the Lambert W function. - Robert Israel, Mar 29 2017

Example

a(3) = 2^4 - 3^3 = 16-27 = -11.

Maple

A215265 := proc(n)
    (n-1)^(n+1)-n^n ;
end proc: # R. J. Mathar, Aug 07 2012

Mathematica

Join[{-2}, Table[(n-1)^(n+1)-n^n, {n, 20}]] (* Harvey P. Dale, May 21 2023 *)

Prog

(Python)
for n in range(33):
    print (n-1)**(n+1) - n**n,

Crossrefs

Cf. A101334, A046065.

Cf. A064232 is essentially equal to (n-1)^(n+1) mod n^n.

Sequence in context: A276116 A306993 A119928 * A036448 A369242 A187111

Adjacent sequences: A215262 A215263 A215264 * A215266 A215267 A215268

Keyword

sign

Author

Alex Ratushnyak, Aug 07 2012

Status

approved