A168675 a(n) = n^8*(n + 1)/2.

0, 1, 384, 13122, 163840, 1171875, 5878656, 23059204, 75497472, 215233605, 550000000, 1286153286, 2794881024, 5710115047, 11068417920, 20503125000, 36507222016, 62781816969, 104689625472, 169835630410, 268800000000, 416051452971, 631072545664

Offset: 0

Author

N. J. A. Sloane, Dec 11 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-45, 120,-210,252,-210,120,-45,10,-1).

Programs

Magma

[n^8*(n+1)/2: n in [0..30]]; // Vincenzo Librandi, Jul 30 2016

Mathematica

Table[n^8(n+1)/2,{n,0,30}] (* Harvey P. Dale, Dec 11 2011 *)
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 1, 384, 13122, 163840, 1171875, 5878656, 23059204, 75497472, 215233605}, 20] (* Vincenzo Librandi, Jul 30 2016 *)

PARI

a(n)=n^8*(n+1)/2 \\ Charles R Greathouse IV, Jul 30 2016

Formula

From Harvey P. Dale, Dec 11 2011: (Start)

a(0)=0, a(1)=1, a(2)=384, a(3)=13122, a(4)=163840, a(5)=1171875, a(6)=5878656, a(7)=23059204, a(8)=75497472, a(9)=215233605, a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10).

G.f.: (x*(x*(x*(x*(x*(x*(x*(128*x + 5281) +38454) +78095) +49780) +9327) +374) + 1))/(1 - x)^10. (End)