cp's OEIS Frontend

A027621 a(n) = n + (n+1)^2 + (n+2)^3 + (n+3)^4.

%I A027621 #31 Aug 07 2022 07:53:51
%S A027621 90,288,700,1440,2646,4480,7128,10800,15730,22176,30420,40768,53550,
%T A027621 69120,87856,110160,136458,167200,202860,243936,290950,344448,405000,
%U A027621 473200,549666,635040,729988,835200,951390,1079296,1219680
%N A027621 a(n) = n + (n+1)^2 + (n+2)^3 + (n+3)^4.
%H A027621 Vincenzo Librandi, <a href="/A027621/b027621.txt">Table of n, a(n) for n = 0..10000</a>
%H A027621 Patrick De Geest, <a href="http://www.worldofnumbers.com/sumpower.htm">Palindromic Quasi_Under_Squares of the form n+(n+1)^2</a>
%H A027621 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A027621 G.f.: 16/(1-x) + 16/(1-x)^2 + 16/(1-x)^3 + 18/(1-x)^4 + 24/(1-x)^5. - _R. J. Mathar_, Feb 22 2008
%F A027621 a(n) = (n+3)^2*(n^2 + 7*n + 10). - _Bruno Berselli_, Aug 05 2011
%F A027621 E.g.f.: (90 + 198*x + 107*x^2 + 19*x^3 + x^4)*exp(x). - _G. C. Greubel_, Aug 05 2022
%p A027621 seq( (n+3)^2*(n^2 + 7*n + 10), n=0..40); # _G. C. Greubel_, Aug 05 2022
%t A027621 Table[Total[Table[(n+i)^(i+1),{i,0,3}]],{n,0,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{90,288,700,1440,2646},40] (* _Harvey P. Dale_, Jun 08 2017 *)
%o A027621 (Sage) [i+(i+1)^2+(i+2)^3+(i+3)^4 for i in range(0,40)] # _Zerinvary Lajos_, Jul 03 2008
%o A027621 (Magma) [n + (n+1)^2 + (n+2)^3 + (n+3)^4: n in [0..40]]; // _Vincenzo Librandi_, Aug 05 2011
%Y A027621 Cf. A000027, A027620, A027622, A028387.
%K A027621 nonn,easy
%O A027621 0,1
%A A027621 _Patrick De Geest_