cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A011851 #27 Jun 14 2023 05:36:59
%S A011851 0,0,0,0,0,0,1,4,11,25,50,92,158,257,400,600,873,1237,1713,2325,3100,
%T A011851 4069,5266,6729,8500,10626,13156,16146,19656,23751,28501,33982,40275,
%U A011851 47467,55651,64926,75398,87179,100388,115151,131601,149879,170133,192519,217201,244351,274150
%N A011851 a(n) = floor(binomial(n,5)/5).
%H A011851 Harvey P. Dale, <a href="/A011851/b011851.txt">Table of n, a(n) for n = 0..1000</a>
%H A011851 <a href="/index/Rec#order_26">Index entries for linear recurrences with constant coefficients</a>, 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).
%F A011851 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]
%p A011851 seq(floor(binomial(n,5)/5), n=0..37); # _Zerinvary Lajos_, Jan 12 2009
%t A011851 Floor[Binomial[Range[0,40],5]/5] (* _Harvey P. Dale_, Jan 21 2013 *)
%t A011851 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 *)
%Y A011851 A column of triangle A011857.
%K A011851 nonn,easy
%O A011851 0,8
%A A011851 _N. J. A. Sloane_
%E A011851 More terms from _Colin Barker_, Jan 23 2013