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 A152297 #21 Apr 07 2022 07:16:40
%S A152297 1,5,79,1427,28447,599435,13100065,293737085,6713171455,155700711995,
%T A152297 3653740285729,86561367835805,2067026079739921,49689509437820933,
%U A152297 1201321507453119103,29187308928225658787,712192597620218620735
%N A152297 Alternate binomial partial sums of binomial(2n,n)*binomial(3n,n) (A006480).
%F A152297 a(n) = sum((-1)^(n-k)*binomial(n,k)*binomial(2*k,k)*binomial(3*k,k),k=0..n).
%F A152297 D-finite with recurrence Recurrence: (n+3)^2*a(n+3)-(24*n^2+120*n+149)*a(n+2)-51*(n+2)^2*a(n+1)-26*(n+1)*(n+2)*a(n)=0.
%F A152297 E.g.f.: exp(-x)*F(1/3,2/3;1,1;27*x), where F(a1,a2;b1;z) is a hypergeometric series.
%F A152297 a(n) ~ 13*sqrt(3) * 26^n / (27*Pi*n). - _Vaclav Kotesovec_, Mar 02 2014
%t A152297 Table[Sum[Binomial[n,k]Binomial[2k,k]Binomial[3k,k](-1)^(n-k),{k,0,n}],{n,0,16}]
%o A152297 (Maxima) makelist(sum((-1)^(n-k)*binomial(n,k)*binomial(2*k,k)*binomial(3*k,k),k,0,n),n,0,16);
%Y A152297 Cf. A006480, A188441, A188918, A188946.
%K A152297 nonn,easy
%O A152297 0,2
%A A152297 _Emanuele Munarini_, Apr 14 2011