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A168351 a(n) = n^5*(n+1)/2.

%I A168351 #18 Mar 20 2025 06:00:08
%S A168351 0,1,48,486,2560,9375,27216,67228,147456,295245,550000,966306,1617408,
%T A168351 2599051,4033680,6075000,8912896,12778713,17950896,24760990,33600000,
%U A168351 44925111,59266768,77236116,99532800,126953125,160398576,200884698
%N A168351 a(n) = n^5*(n+1)/2.
%H A168351 Vincenzo Librandi, <a href="/A168351/b168351.txt">Table of n, a(n) for n = 0..10000</a>
%H A168351 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A168351 a(n) = Sum_{i=1..n} Sum_{j=1..n} Sum_{k=1..n} Sum_{l=1..n} Sum_{m=1..n} (i+j+k-l-m). - _Wesley Ivan Hurt_, Aug 13 2015
%F A168351 From _G. C. Greubel_, Mar 20 2025: (Start)
%F A168351 G.f.: x*(1 + 41*x + 171*x^2 + 131*x^3 + 16*x^4)/(1-x)^7.
%F A168351 E.g.f.: (1/2)*x*(2 + 46*x + 115*x^2 + 75*x^3 + 16*x^4 + x^5)*exp(x). (End)
%t A168351 Table[n^5*(n + 1)/2, {n, 0, 40}] (* _Wesley Ivan Hurt_, Aug 13 2015 *)
%o A168351 (Magma) [n^5*(n+1)/2: n in [0..30]]; // _Vincenzo Librandi_, Aug 28 2011
%o A168351 (SageMath)
%o A168351 def A168351(n): return n^4*binomial(n+1,2)
%o A168351 print([A168351(n) for n in range(41)]) # _G. C. Greubel_, Mar 20 2025
%Y A168351 Sequences of the form n^5*(n^k + 1)/2: A000584 (k=0), this sequence (k=1), A168364 (k=2), A168371 (k=3), A168372 (k=4), A071236 (k=5), A168412 (k=6), A168432 (k=7), A168462 (k=8), A168471 (k=9), A168507 (k=10).
%K A168351 nonn,easy
%O A168351 0,3
%A A168351 _N. J. A. Sloane_, Dec 11 2009