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a(1)=1, a(2)=2, a(3)=4, a(n)=C(C(a(n-1),a(n-2)),C(a(n-1),a(n-2))).
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%I #4 Mar 31 2012 14:40:13

%S 1,2,4,15,8885554239441880

%N a(1)=1, a(2)=2, a(3)=4, a(n)=C(C(a(n-1),a(n-2)),C(a(n-1),a(n-2))).

%C Next term has 306322 digits. For a(1)=1, a(2)=2 and a(3)=1,2,3, sequence ends with 1's: 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,... 1, 2, 2, 0, 0, 1, 1, 1, 1, 1, 1, 1,... 1, 2, 3, 3, 0, 0, 1, 1, 1, 1, 1, 1,...

%t a=1;b=2;c=4;s={a,b,c}; Do[d=Binomial[Binomial[c,b], Binomial[b,a]];AppendTo[s,d];a=b;b=c;c=d,{3}];s IntegerDigits[s[[ -1]]]//Length 306322

%K nonn

%O 1,2

%A _Zak Seidov_, Jan 05 2007