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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)=a(2)=1 and a(3)=4.
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%I #7 Jul 21 2019 07:42:33

%S 1,1,4,4,4,4,20,36,52,132,292,580,1252,2628,6196,13412,28884,64516,

%T 147140,327684,722116,1615236,3758292,8500772,19027572,43203204,

%U 100782308,230210884,522001572,1193084612,2800307188,6441467748,14722404372

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

%K nonn

%O 1,3

%A _Clark Kimberling_