A011930 a(n) = floor(n(n-1)(n-2)(n-3)/20).

0, 0, 0, 0, 1, 6, 18, 42, 84, 151, 252, 396, 594, 858, 1201, 1638, 2184, 2856, 3672, 4651, 5814, 7182, 8778, 10626, 12751, 15180, 17940, 21060, 24570, 28501, 32886, 37758, 43152, 49104, 55651, 62832, 70686, 79254, 88578, 98701

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1, 1, -4, 6, -4, 1).

Programs

Magma

[Floor(n*(n-1)*(n-2)*(n-3)/20  ): n in [0..40]]; // Vincenzo Librandi, Jun 19 2012

Mathematica

CoefficientList[Series[x^4*(x^4+2*x^3+2*x+1)/((1-x)^5*(x^4+x^3+x^2+x+1)),{x,0,50}],x] (* Vincenzo Librandi, Jun 19 2012 *)
Table[Floor[n(n-1)(n-2)(n-3)/20],{n,0,40}] (* or *) LinearRecurrence[ {4,-6,4,-1,1,-4,6,-4,1},{0,0,0,0,1,6,18,42,84},40] (* Harvey P. Dale, Apr 08 2013 *)

Formula

From R. J. Mathar, Apr 15 2010: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-5) - 4*a(n-6) + 6*a(n-7) - 4*a(n-8) + a(n-9).

G.f.: x^4*(x^4+2*x^3+2*x+1) / ((1-x)^5*(x^4+x^3+x^2+x+1)). (End)