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a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=2 and a(2)=a(3)=1.
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%I #6 Jul 21 2019 18:23:18

%S 2,1,1,2,4,8,18,40,88,194,460,1080,2514,5840,14256,34450,82552,197696,

%T 489714,1204736,2945128,7188018,18002376,44805640,110894770,274209616,

%U 691588200,1736001314,4338383356,10827952192,27470096770,69388005832

%N a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=2 and a(2)=a(3)=1.

%K nonn

%O 1,1

%A _Clark Kimberling_