A215265 a(n) = (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, 10769816560735764585313397

Offset: 0

Author

Alex Ratushnyak, Aug 07 2012

Keywords

• sign

Comments

0^0 is interpreted as 1.

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..386

Crossrefs

Cf. A101334, A046065.

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

Programs

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 *)

Python

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

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