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A091759 a(n) = 0^n + 2((n+1)^n - (-1)^n) / (n+2). 0
1, 2, 4, 26, 208, 2222, 29412, 466034, 8609344, 181818182, 4322904100, 114308980106, 3328297874640, 105828636433886, 3649115753173828, 135637824071393762, 5406799097296318720, 230095953656704898102 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

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).

MAPLE

seq(0^n + 2*((n+1)^n-(-1)^n)/(n+2), n=0..20); # Georg Fischer, May 08 2021

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 *)

PROG

(PARI) a(n) = 0^n + 2*((n+1)^n - (-1)^n) / (n+2); \\ Michel Marcus, May 09 2021

CROSSREFS

Cf. A083063.

Sequence in context: A215882 A032328 A019034 * A262067 A193480 A032076

Adjacent sequences:  A091756 A091757 A091758 * A091760 A091761 A091762

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Feb 03 2004

STATUS

approved

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Last modified October 27 13:38 EDT 2021. Contains 348276 sequences. (Running on oeis4.)