%I #18 Mar 20 2025 06:00:08

%S 0,1,48,486,2560,9375,27216,67228,147456,295245,550000,966306,1617408,

%T 2599051,4033680,6075000,8912896,12778713,17950896,24760990,33600000,

%U 44925111,59266768,77236116,99532800,126953125,160398576,200884698

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

%H Vincenzo Librandi, <a href="/A168351/b168351.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F 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 From _G. C. Greubel_, Mar 20 2025: (Start)

%F G.f.: x*(1 + 41*x + 171*x^2 + 131*x^3 + 16*x^4)/(1-x)^7.

%F E.g.f.: (1/2)*x*(2 + 46*x + 115*x^2 + 75*x^3 + 16*x^4 + x^5)*exp(x). (End)

%t Table[n^5*(n + 1)/2, {n, 0, 40}] (* _Wesley Ivan Hurt_, Aug 13 2015 *)

%o (Magma) [n^5*(n+1)/2: n in [0..30]]; // _Vincenzo Librandi_, Aug 28 2011

%o (SageMath)

%o def A168351(n): return n^4*binomial(n+1,2)

%o print([A168351(n) for n in range(41)]) # _G. C. Greubel_, Mar 20 2025

%Y 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 nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Dec 11 2009