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A191012 a(n) = n^5 - n^4 + n^3 - n^2 + n. 1

%I

%S 0,1,22,183,820,2605,6666,14707,29128,53145,90910,147631,229692,

%T 344773,501970,711915,986896,1340977,1790118,2352295,3047620,3898461,

%U 4929562,6168163,7644120,9390025,11441326,13836447,16616908,19827445

%N a(n) = n^5 - n^4 + n^3 - n^2 + n.

%C n such that x^5 + x^4 + x^3 + x^2 + x + n factors over the integers.

%H Vincenzo Librandi, <a href="/A191012/b191012.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F a(n) = n*A060884(n).

%F G.f.: x*(5*x^4 + 32*x^3 + 66*x^2 + 16*x + 1)/(1-x)^6.

%e a(2) = 22 is in the sequence, because x^5 + x^4 + x^3 + x^2 + x + 22 = (x+2)*(x^4 - x^3 + 3*x^2 - 5*x + 11).

%p [seq(n*(n^4-n^3+n^2-n+1),n=0..25)];

%o (PARI) a(n)=((((n-1)*n+1)*n-1)*n+1)*n \\ _Charles R Greathouse IV_, Jun 17 2011

%o (Magma) [n^5 - n^4 + n^3 - n^2 + n: n in [0..30]]; // _Vincenzo Librandi_, Jun 18 2011

%Y Cf. A060884.

%K easy,nonn

%O 0,3

%A _Franz Vrabec_, Jun 16 2011

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Last modified January 30 12:56 EST 2023. Contains 359945 sequences. (Running on oeis4.)