cp's OEIS Frontend

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

%I A215265 #21 Jul 04 2025 16:53:51
%S A215265 -2,-1,-3,-11,-13,971,31469,856073,23576391,686321335,21381059609,
%T A215265 714688329389,25606611695675,981043357956611,40073886188532741,
%U A215265 1740059447428511761,80079381261983807759,3895126220983308449519,199726027609854787271729,10769816560735764585313397
%N A215265 a(n) = (n-1)^(n+1) - n^n.
%C A215265 0^0 is interpreted as 1.
%H A215265 Alois P. Heinz, <a href="/A215265/b215265.txt">Table of n, a(n) for n = 0..386</a>
%F A215265 For n>0, a(n) = A046065(n-1) - A101334(n).
%F A215265 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
%e A215265 a(3) = 2^4 - 3^3 = 16-27 = -11.
%p A215265 A215265 := proc(n)
%p A215265     (n-1)^(n+1)-n^n ;
%p A215265 end proc: # _R. J. Mathar_, Aug 07 2012
%t A215265 Join[{-2},Table[(n-1)^(n+1)-n^n,{n,20}]] (* _Harvey P. Dale_, May 21 2023 *)
%o A215265 (Python)
%o A215265 for n in range(33):
%o A215265     print((n-1)**(n+1) - n**n)
%Y A215265 Cf. A101334, A046065.
%Y A215265 Cf. A064232 is essentially equal to (n-1)^(n+1) mod n^n.
%K A215265 sign
%O A215265 0,1
%A A215265 _Alex Ratushnyak_, Aug 07 2012