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a(n) = (n+1)*(14*n^3+13*n^2+6*n+1).
1

%I #13 Oct 21 2022 21:20:20

%S 1,68,531,2056,5645,12636,24703,43856,72441,113140,168971,243288,

%T 339781,462476,615735,804256,1033073,1307556,1633411,2016680,2463741,

%U 2981308,3576431,4256496,5029225,5902676

%N a(n) = (n+1)*(14*n^3+13*n^2+6*n+1).

%H Harvey P. Dale, <a href="/A027850/b027850.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(0)=1, a(1)=68, a(2)=531, a(3)=2056, a(4)=5645, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5) _Harvey P. Dale_, May 21 2012

%F G.f.: (-71*x^3-201*x^2-63*x-1)/(x-1)^5 _Harvey P. Dale_, May 21 2012

%t (* From _Harvey P. Dale_, May 21 2012: (Start) *)

%t Table[(n+1) (14 n^3+13 n^2+6 n+1),{n,0,30}]

%t LinearRecurrence[ {5,-10,10,-5,1},{1,68,531,2056,5645},30] (* End *)

%o (PARI) a(n)=(n+1)*(14*n^3+13*n^2+6*n+1) \\ _Charles R Greathouse IV_, Oct 21 2022

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.