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A072025 a(n) = n^4 + 2*n^3 + 4*n^2 + 3*n + 1 = ((n+1)^5+n^5) / (2*n+1). 4

%I

%S 1,11,55,181,461,991,1891,3305,5401,8371,12431,17821,24805,33671,

%T 44731,58321,74801,94555,117991,145541,177661,214831,257555,306361,

%U 361801,424451,494911,573805,661781,759511,867691,987041,1118305,1262251,1419671,1591381

%N a(n) = n^4 + 2*n^3 + 4*n^2 + 3*n + 1 = ((n+1)^5+n^5) / (2*n+1).

%H Vincenzo Librandi, <a href="/A072025/b072025.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F From _Colin Barker_, Dec 01 2015: (Start)

%F a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n>4.

%F G.f.: (1+x)^2*(1+4*x+x^2) / (1-x)^5.

%F (End)

%t Table[((n+1)^5+n^5)/(2n+1),{n,0,30}] (* _Vincenzo Librandi_, Nov 23 2011 *)

%t LinearRecurrence[{5,-10,10,-5,1},{1,11,55,181,461},50] (* _Harvey P. Dale_, Dec 14 2019 *)

%o (MAGMA) [((n+1)^5+n^5)/(2*n+1): n in [0..40]]; // _Vincenzo Librandi_, Nov 23 2011

%o (PARI) a(n)=n^4+2*n^3+4*n^2+3*n+1 \\ _Charles R Greathouse IV_, Nov 23 2011

%o (PARI) Vec((1+x)^2*(1+4*x+x^2)/(1-x)^5 + O(x^100)) \\ _Colin Barker_, Dec 01 2015

%Y Cf. A022521, A072024.

%K nonn,easy,less

%O 0,2

%A _Henry Bottomley_, Jun 06 2002

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Last modified July 25 11:18 EDT 2021. Contains 346289 sequences. (Running on oeis4.)