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 A277188 #13 Oct 06 2016 15:50:09
%S A277188 1,7,43,281,1896,13112,92359,659941,4769758,34797170,255838760,
%T A277188 1893389720,14091400480,105385445856,791504226943,5966958725021,
%U A277188 45133376297922,342400478465678,2604549070175770,19860078537996958,151769147958738016
%N A277188 The binomial sum a(n) = Sum_{k=0..n}(binomial(n,k)*binomial(n+1,k+1)*binomial(n+2,k+2)).
%F A277188 a(n) = (1/2)*(n+1)^2*(n+2)*hypergeometric({-n,-n,-n},{2,3},-1).
%F A277188 From _Vaclav Kotesovec_, Oct 04 2016: (Start)
%F A277188 Recurrence: (n+2)^2*(6*n^3 + 3*n^2 - 3*n - 2)*a(n) = (42*n^5 + 147*n^4 + 147*n^3 - 8*n^2 - 60*n - 16)*a(n-1) + 8*(n-1)*n*(6*n^3 + 21*n^2 + 21*n + 4)*a(n-2).
%F A277188 a(n) ~ 2^(3*n+4)/(sqrt(3)*Pi*n).
%F A277188 (End)
%t A277188 Table[Sum[Binomial[n,k]Binomial[n+1,k+1]Binomial[n+2,k+2],{k,0,n}],{n,0,100}]
%o A277188 (Maxima) makelist((n+1)^2*(n+2)/2*hypergeometric([-n,-n,-n],[2,3],-1),n,0,12);
%o A277188 (PARI) a(n) = sum(k=0, n, (binomial(n,k)*binomial(n+1,k+1)*binomial(n+2,k+2))); \\ _Michel Marcus_, Oct 04 2016
%K A277188 nonn
%O A277188 0,2
%A A277188 _Emanuele Munarini_, Oct 04 2016