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%I #15 May 14 2022 03:54:49
%S 0,2,144,1944,12800,56250,190512,537824,1327104,2952450,6050000,
%T 11595672,21026304,36386714,60505200,97200000,151519232,230016834,
%U 341067024,495219800,705600000,988352442,1363135664,1853666784
%N a(n) = n^5*(n+1)^2/2.
%C Row sums of triangle A163285.
%H G. C. Greubel, <a href="/A163275/b163275.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F From _R. J. Mathar_, Feb 05 2010: (Start)
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).
%F G.f.: 2*x*(1 + 64*x + 424*x^2 + 584*x^3 + 179*x^4 +8*x^5)/(x-1)^8. (End)
%F From _Amiram Eldar_, May 14 2022: (Start)
%F Sum_{n>=1} 1/a(n) = 12 -5*Pi^2/3 - 2*Pi^4/45 + 6*zeta(3) + 2*zeta(5).
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 20*log(2) + 9*zeta(3)/2 + 15*zeta(5)/8 - 12 - Pi^2/2 - 7*Pi^4/180. (End)
%p A163275 := proc(n) n^5*(n+1)^2/2 ; end proc: seq(A163275(n),n=0..60) ; # _R. J. Mathar_, Feb 05 2010
%t Table[(1/2)*n^5*(n + 1)^2, {n,0,50}] (* or *) LinearRecurrence[{8,-28,56, -70,56,-28,8,-1}, {0,2,144,1944,12800,56250,190512,537824}, 50] (* _G. C. Greubel_, Dec 12 2016 *)
%o (PARI) concat([0], Vec(2*x*(1+64*x+424*x^2+584*x^3+179*x^4+8*x^5)/(x-1)^8 + O(x^50))) \\ _G. C. Greubel_, Dec 12 2016
%Y Cf. A006002, A099903, A163102, A163274, A163276, A163277, A163285.
%K easy,nonn
%O 0,2
%A _Omar E. Pol_, Jul 24 2009
%E Extended by _R. J. Mathar_, Feb 05 2010
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