A091759 a(n) = 0^n + 2((n+1)^n - (-1)^n) / (n+2).
1, 2, 4, 26, 208, 2222, 29412, 466034, 8609344, 181818182, 4322904100, 114308980106, 3328297874640, 105828636433886, 3649115753173828, 135637824071393762, 5406799097296318720, 230095953656704898102
Offset: 0
Crossrefs
Cf. A083063.
Programs
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Maple
seq(0^n + 2*((n+1)^n-(-1)^n)/(n+2),n=0..20); # Georg Fischer, May 08 2021
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Mathematica
P[n_,m_,z_]:= Product[z - Sum[E^(j*k*2*pi*I/n), {k,1,m}], {j,0,n-1}]; Table[FullSimplify[P[n,n-2,n]], {n,0,12}] (* Georg Fischer, May 08 2021 *) -
PARI
a(n) = 0^n + 2*((n+1)^n - (-1)^n) / (n+2); \\ Michel Marcus, May 09 2021
Formula
a(n) = P(n, n-2, n) where P(n, m, z) = Product_{j=0..n-1} (z - Sum_{k=1..m} e^(j*k*2*Pi*I/n)), I=sqrt(-1).