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

%I #26 Aug 05 2024 08:40:47

%S 0,2,15,60,170,390,777,1400,2340,3690,5555,8052,11310,15470,20685,

%T 27120,34952,44370,55575,68780,84210,102102,122705,146280,173100,

%U 203450,237627,275940,318710,366270,418965,477152,541200,611490,688415,772380,863802,963110

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

%D T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.

%H Vincenzo Librandi, <a href="/A071237/b071237.txt">Table of n, a(n) for n = 0..2000</a>

%F From _Arkadiusz Wesolowski_, Apr 01 2012: (Start)

%F a(n) = A000217(n)*A002522(n).

%F a(0) = 0, a(1) = 2; for n >= 2, a(n) = ceiling(n^5/(2*n-2)) - 1.

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

%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, a(0)=0, a(1)=2, a(2)=15, a(3)=60, a(4)=170. - _Yosu Yurramendi_, Sep 03 2013

%F E.g.f.: (1/2)*x*(4 + 11*x + 7*x^2 + x^3)*exp(x). - _G. C. Greubel_, Aug 05 2024

%t Table[(n^4 + n^3 + n^2 + n)/2, {n, 0, 60}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 07 2011 *)

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

%o (SageMath)

%o def A071237(n): return (n^2+1)*binomial(n+1,2)

%o [A071237(n) for n in range(51)] # _G. C. Greubel_, Aug 05 2024

%Y Cf. A027445, A037270.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Jun 12 2002