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 A025277 #25 Feb 04 2025 17:48:32
%S A025277 0,0,1,1,0,1,2,1,2,6,6,7,20,30,34,75,140,182,322,644,972,1554,3024,
%T A025277 5091,8052,14784,26378,43032,75504,136994,232232,399399,720356,
%U A025277 1257256,2161874,3852576,6831552,11858418,20949304,37350768
%N A025277 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 5, with initial values 0,0,1,1.
%F A025277 G.f.: -(sqrt(1-4*x^4-4*x^3)-1)/2. - _Vladimir Kruchinin_, Nov 21 2014
%F A025277 a(n) = sum(m=0..(n-3)/2, (binomial(n-2*m-3,m)*binomial(2*m+1,n-2*m-3))/(2*m+1)). - _Vladimir Kruchinin_, Nov 21 2014
%F A025277 a(n) = (4 - 24/n)*a(n-4) + (4 - 18/n)*a(n-3). - _Robert Israel_, Nov 21 2014
%p A025277 A025277:= gfun:-rectoproc({a(n) = (4 - 24/n)*a(n-4) + (4 - 18/n)*a(n-3), a(1)=0,a(2)=0,a(3)=1,a(4)=1},a(n),remember):
%p A025277 seq(A025277(n),n=1..100); # _Robert Israel_, Nov 21 2014
%t A025277 nmax = 30; aa = ConstantArray[0,nmax]; aa[[1]] = 0; aa[[2]] = 0; aa[[3]] = 1; aa[[4]] = 1; Do[aa[[n]] = Sum[aa[[k]]*aa[[n-k]],{k,1,n-1}],{n,5,nmax}]; aa (* _Vaclav Kotesovec_, Jan 25 2015 *)
%t A025277 a[n_] := Sum[Binomial[n-2*m-3, m]*Binomial[2*m+1, n-2*m-3]/(2*m+1), {m, 0, (n-3)/2}]; Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Apr 03 2015, after _Vladimir Kruchinin_ *)
%o A025277 (Maxima)
%o A025277 a(n):=sum((binomial(n-2*m-3,m)*binomial(2*m+1,n-2*m-3))/(2*m+1),m,0,(n-3)/2); /* _Vladimir Kruchinin_, Nov 21 2014 */
%K A025277 nonn
%O A025277 1,7
%A A025277 _Clark Kimberling_