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a(n) = A166231(n)/4^n.
5

%I #7 May 08 2016 00:40:38

%S 1,1,3,20,272,7424,405504,44302336,9680453632,4230542786560,

%T 3697657604210688,6463791365183504384,22598414411798807576576,

%U 158015104883301198495481856,2209780998563745292895322636288

%N a(n) = A166231(n)/4^n.

%C a(n+1) is the Hankel transform of A068764.

%H G. C. Greubel, <a href="/A166232/b166232.txt">Table of n, a(n) for n = 0..70</a>

%F a(n) = 2^C(n,2)*Sum_{k=0..floor(n/2)} C(n,2k)*2^(-k).

%F a(n) = A166231(n)/4^n.

%t Table[2^(Binomial[n, 2])*Sum[Binomial[n, 2 k]*2^(-k), {k, 0, Floor[n/2]}], {n, 0, 25}] (* _G. C. Greubel_, May 07 2016 *)

%Y Cf. A068764, A166231.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Oct 09 2009