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a(n) = ((n-1)^(n+1) + (-1)^n*(n+1)^(n-1))/(n^2).
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%I #10 Jun 06 2021 06:01:42

%S -1,1,0,23,112,2637,28928,705259,12021504,337390073,7752749056,

%T 252186614847,7261683740672,271082082053317,9359536638984192,

%U 396049017137512403,15920162462882529280,754792662169555947633,34587513064809080815616,1818644980834260579498343

%N a(n) = ((n-1)^(n+1) + (-1)^n*(n+1)^(n-1))/(n^2).

%C a(2n) = A233446(n) = ((2n-1)^(2n+1) + (2n+1)^(2n-1))/(2n)^2 = A154682(n)/(2n)^2 for n > 0.

%F a(n) = ((n-1)^(n+1) + (-1)^n*(n+1)^(n-1))/(n^2).

%t Table[((m-1)^(m+1)+(-1)^m*(m+1)^(m-1))/(m^2),{m,1,20}]

%o (PARI) a(n) = ((n-1)^(n+1) + (-1)^n*(n+1)^(n-1))/n^2; \\ _Michel Marcus_, Jun 06 2021

%Y Cf. A154682, A233446.

%K sign

%O 1,4

%A _Alexander Adamchuk_, Dec 22 2013