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 A095667 #28 Aug 27 2014 06:26:24
%S A095667 4,17,45,95,175,294,462,690,990,1375,1859,2457,3185,4060,5100,6324,
%T A095667 7752,9405,11305,13475,15939,18722,21850,25350,29250,33579,38367,
%U A095667 43645,49445,55800,62744,70312,78540,87465,97125,107559,118807,130910,143910,157850
%N A095667 Fifth column (m=4) of (1,4)-Pascal triangle A095666.
%C A095667 If Y is a 4-subset of an n-set X then, for n>=7, a(n-7) is the number of 4-subsets of X having at most one element in common with Y. - _Milan Janjic_, Dec 08 2007
%C A095667 In this sequence if we do a forward difference, then the 3rd forward difference when considered as a sequence will be an arithmetic progression with common difference 1. The same way the sequence formed by the 3rd forward difference of A047668 will be an arithmetic progression with common difference 8. [From Gopalakrishnan (gopala498(AT)yahoo.co.in), Jun 05 2010]
%C A095667 Row 4 of the convolution array A213550. [_Clark Kimberling_, Jun 20 2012]
%F A095667 G.f.: (4-3*x)/(1-x)^5.
%F A095667 a(n) = 4*b(n)-3*b(n-1) = (n+16)*binomial(n+3, 3)/4, with b(n):=binomial(n+4, 4)= A000332(n+4, 4).
%F A095667 a(n) = sum_{k=1..n} ( sum_{i=1..k} i*(n-k+4) ). - _Wesley Ivan Hurt_, Sep 25 2013
%p A095667 A095667:=n->(n+16)*binomial(n+3,3)/4; seq(A095667(k), k=0..70); # _Wesley Ivan Hurt_, Sep 25 2013
%t A095667 s1=s2=s3=s4=0;lst={};Do[a=n+(n+2);s1+=a;s2+=s1;s3+=s2;s4+=s3;AppendTo[lst,s3/2],{n,3,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 04 2009 *)
%Y A095667 Partial sums of A060488.
%K A095667 nonn,easy
%O A095667 0,1
%A A095667 _Wolfdieter Lang_, Jun 11 2004