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A025264 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 4, starting 2,1,1.

%I A025264 #15 Jan 13 2025 11:11:00
%S A025264 2,1,1,5,22,99,450,2067,9586,44852,211570,1005427,4810460,23157904,
%T A025264 112110906,545524287,2666864340,13092764136,64527778938,319157531592,
%U A025264 1583724160896,7882364163954,39339994155288,196843821874407,987272738842392
%N A025264 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 4, starting 2,1,1.
%F A025264 G.f.: (1-sqrt(1-8*x+12*x^2+12*x^3))/2. - _Michael Somos_, Jun 08 2000
%F A025264 Recurrence: n*a(n) = 4*(2*n-3)*a(n-1) - 12*(n-3)*a(n-2) - 6*(2*n-9)*a(n-3). - _Vaclav Kotesovec_, Jan 25 2015
%p A025264 A025264 := proc(n)
%p A025264     option remember ;
%p A025264     if n < 4 then
%p A025264         op(n,[2,1,1]) ;
%p A025264     else
%p A025264         add( procname(i)*procname(n-i),i=1..n-1) ;
%p A025264     end if;
%p A025264 end proc:
%p A025264 seq(A025264(n),n=1..20) ; # _R. J. Mathar_, Jan 13 2025
%t A025264 nmax = 30; aa = ConstantArray[0,nmax]; aa[[1]] = 2; aa[[2]] = 1; aa[[3]] = 1; Do[aa[[n]] = Sum[aa[[k]] * aa[[n-k]],{k,1,n-1}],{n,4,nmax}]; aa (* _Vaclav Kotesovec_, Jan 25 2015 *)
%o A025264 (PARI) a(n)=polcoeff((1-sqrt(1-8*x+12*x^2+12*x^3+x*O(x^n)))/2,n)
%Y A025264 Cf. A025266.
%K A025264 nonn
%O A025264 1,1
%A A025264 _Clark Kimberling_