A011851 a(n) = floor(binomial(n,5)/5).

0, 0, 0, 0, 0, 0, 1, 4, 11, 25, 50, 92, 158, 257, 400, 600, 873, 1237, 1713, 2325, 3100, 4069, 5266, 6729, 8500, 10626, 13156, 16146, 19656, 23751, 28501, 33982, 40275, 47467, 55651, 64926, 75398, 87179, 100388, 115151, 131601, 149879, 170133, 192519, 217201, 244351, 274150

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 5, 5, -15, 20, -15, 5, 5, -15, 20, -15, 5, 5, -15, 20, -15, 5, 5, -15, 20, -15, 6, -1).

Crossrefs

A column of triangle A011857.

Programs

Maple

seq(floor(binomial(n,5)/5), n=0..37); # Zerinvary Lajos, Jan 12 2009

Mathematica

Floor[Binomial[Range[0,40],5]/5] (* Harvey P. Dale, Jan 21 2013 *)
CoefficientList[Series[x^6 (x^19 - 4 x^18 + 8 x^17 - 8 x^16 + 4 x^15 - 3 x^13 + 6 x^12 - 6 x^11 + 3 x^10 - 2 x^8 + 4 x^7 - 4 x^6 + 2 x^5 - x^3 + 2 x^2 - 2 x + 1)/((x - 1)^6 (x^20 + x^15 + x^10 + x^5 + 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 15 2013 *)

Formula

G.f.: x^6*(x^19 -4*x^18 +8*x^17 -8*x^16 +4*x^15 -3*x^13 +6*x^12 -6*x^11 +3*x^10 -2*x^8 +4*x^7 -4*x^6 +2*x^5 -x^3 +2*x^2 -2*x +1) / ((x -1)^6*(x^20 +x^15 +x^10 +x^5 +1)). [Colin Barker, Jan 23 2013]

Extensions

More terms from Colin Barker, Jan 23 2013