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A163275
a(n) = n^5*(n+1)^2/2.
6
0, 2, 144, 1944, 12800, 56250, 190512, 537824, 1327104, 2952450, 6050000, 11595672, 21026304, 36386714, 60505200, 97200000, 151519232, 230016834, 341067024, 495219800, 705600000, 988352442, 1363135664, 1853666784
OFFSET
0,2
COMMENTS
Row sums of triangle A163285.
FORMULA
From R. J. Mathar, Feb 05 2010: (Start)
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).
G.f.: 2*x*(1 + 64*x + 424*x^2 + 584*x^3 + 179*x^4 +8*x^5)/(x-1)^8. (End)
From Amiram Eldar, May 14 2022: (Start)
Sum_{n>=1} 1/a(n) = 12 -5*Pi^2/3 - 2*Pi^4/45 + 6*zeta(3) + 2*zeta(5).
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)
MAPLE
A163275 := proc(n) n^5*(n+1)^2/2 ; end proc: seq(A163275(n), n=0..60) ; # R. J. Mathar, Feb 05 2010
MATHEMATICA
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 *)
PROG
(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
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Jul 24 2009
EXTENSIONS
Extended by R. J. Mathar, Feb 05 2010
STATUS
approved