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.
%I A096942 #23 Aug 29 2024 06:04:25
%S A096942 5,21,55,115,210,350,546,810,1155,1595,2145,2821,3640,4620,5780,7140,
%T A096942 8721,10545,12635,15015,17710,20746,24150,27950,32175,36855,42021,
%U A096942 47705,53940,60760,68200,76296,85085,94605,104895,115995,127946,140790,154570,169330,185115
%N A096942 Fifth column of (1,5)-Pascal triangle A096940.
%C A096942 If Y is a 5-subset of an n-set X then, for n>=8, a(n-8) is the number of 4-subsets of X having at most one element in common with Y. - _Milan Janjic_, Dec 08 2007
%H A096942 Vincenzo Librandi, <a href="/A096942/b096942.txt">Table of n, a(n) for n = 0..1000</a>
%F A096942 a(n) = (n+20)*binomial(n+3, 3)/4 = 5*b(n) - 4*b(n-1), with b(n) = A000332(n+4) = binomial(n+4, 4).
%F A096942 G.f.: (5-4*x)/(1-x)^5.
%F A096942 a(n) = Sum_{k=1..n} (Sum_{i=1..k} i*(n-k+5)). - _Wesley Ivan Hurt_, Sep 26 2013
%t A096942 Table[(n + 20) Binomial[n + 3, 3]/4, {n, 0, 100}]
%t A096942 CoefficientList[Series[(5 - 4 x)/(1 - x)^5, {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 01 2013 *)
%o A096942 (Magma) [(n + 20)*Binomial(n + 3, 3) div 4: n in [0..50]]; // _Vincenzo Librandi_, Oct 01 2013
%Y A096942 Fourth column: A096941; sixth column: A096943.
%K A096942 nonn,easy
%O A096942 0,1
%A A096942 _Wolfdieter Lang_, Jul 16 2004