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%I #21 Sep 08 2022 08:45:48
%S 1,7,41,151,409,911,1777,3151,5201,8119,12121,17447,24361,33151,44129,
%T 57631,74017,93671,117001,144439,176441,213487,256081,304751,360049,
%U 422551,492857,571591,659401,756959,864961,984127,1115201,1258951,1416169,1587671
%N a(n) = 1 + 2*n + n^2 + 2*n^3 + n^4.
%C Also binomial transform of the quasi-finite sequence 1,6,28,48,24,0 (0 continued).
%H Vincenzo Librandi, <a href="/A165563/b165563.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1)
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + 24 -> 4th differences are 24 = A010863(n).
%F G.f.: (-1 - 2*x - 16*x^2 - 6*x^3 + x^4)/(x-1)^5.
%t Table[1+2n+n^2+2n^3+n^4,{n,0,50}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,7,41,151,409},50] (* _Harvey P. Dale_, Nov 13 2021 *)
%o (Magma) [1 +2*n +n^2 +2*n^3 +n^4: n in [0..40] ]; // _Vincenzo Librandi_, Aug 06 2011
%o (PARI) a(n)=1+2*n+n^2+2*n^3+n^4 \\ _Charles R Greathouse IV_, Oct 16 2015
%K nonn,easy
%O 0,2
%A _Paul Curtz_, Sep 22 2009
%E Edited and extended by _R. J. Mathar_, Sep 25 2009