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a(1) = 3, a(2n) = a(2n-1)*(a(2n-1)+1)/2, a(2n+1) = a(2n)*(a(2n)-1)/2.
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%I #8 Aug 15 2019 07:27:29

%S 3,6,15,120,7140,25493370,324955944231765,

%T 52798182845779144865989623495,

%U 1393824055908163580110066696496417846029512708072933195765,971372749414141756744711053350258180262238679505115309556108472465628097348257583700704919225793663496284373565495

%N a(1) = 3, a(2n) = a(2n-1)*(a(2n-1)+1)/2, a(2n+1) = a(2n)*(a(2n)-1)/2.

%C a(10) has 114 digits; a(11) has 228 digits. - _Emeric Deutsch_, Oct 06 2005

%p a:=proc(n) if n=1 then 3 elif n mod 2 = 0 then a(n-1)*(a(n-1)+1)/2 else a(n-1)*(a(n-1)-1)/2 fi end: seq(a(n),n=1..10); # _Emeric Deutsch_, Oct 06 2005

%K easy,nonn

%O 1,1

%A _Amarnath Murthy_, Aug 14 2005

%E More terms from _Emeric Deutsch_, Oct 06 2005