%I #18 Sep 08 2022 08:46:07

%S 1,1,15,49,109,201,331,505,729,1009,1351,1761,2245,2809,3459,4201,

%T 5041,5985,7039,8209,9501,10921,12475,14169,16009,18001,20151,22465,

%U 24949,27609,30451,33481,36705,40129,43759,47601,51661,55945,60459,65209,70201,75441,80935,86689,92709,99001,105571,112425,119569

%N n^3 + 4*n^2 - 5*n + 1.

%H Vincenzo Librandi, <a href="/A241577/b241577.txt">Table of n, a(n) for n = 0..1000</a>

%H Adalbert Kerber, <a href="http://dx.doi.org/10.1016/0012-365X(78)90163-2">A matrix of combinatorial numbers related to the symmetric groups</a>, Discrete Math., 21 (1978), 319-321. See Eq. (7), col. 4.

%H A. Kerber, <a href="/A004211/a004211.pdf">A matrix of combinatorial numbers related to the symmetric groups<</a>, Discrete Math., 21 (1978), 319-321. [Annotated scanned copy]

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F G.f.: (1-3*x+17*x^2-9*x^3)/(1-x)^4. - _Vincenzo Librandi_, Apr 28 2014

%F Recurrence: a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Fung Lam_, May 11 2014

%t CoefficientList[Series[(1 - 3 x + 17 x^2 - 9 x^3)/(1 - x)^4, {x, 0, 50}], x] (* _Vincenzo Librandi_, Apr 28 2014 *)

%o (Magma) [n^3+4*n^2-5*n+1: n in [0..50]]; // _Vincenzo Librandi_, Apr 28 2014

%o (PARI) a(n)=n^3+4*n^2-5*n+1 \\ _Charles R Greathouse IV_, Aug 26 2014

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Apr 27 2014