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%I #5 Mar 30 2012 18:36:44
%S 1,2,5,12,30,73,169,377,831,1842,4110,9136,20006,42906,90148,186414,
%T 381955,780966,1603330,3319952,6949554,14704880,31379910,67272276,
%U 144212735,307752571,651353609,1363714711,2820488954,5761343912
%N Binomial transform of A101910, where A101910(n) = a(A000120(n-1)) for n>0 with A101910(0) = 1.
%C Also gives the records in A101910 at positions 2^n for n>=0. A000120 is the binary 1's-counting sequence.
%F a(n) = 1 + Sum_{k=0, n-1} C(n, k)*a(A000120(n-k-1)) for n>0, a(0)=1. a(n) = A101910(2^n) for n>=0.
%e Equals the binomial transform of A101910, where
%e A101910 = {1,1,2,2,5,2,5,5,12,2,5,5,12,5,12,12,30,...}
%e which has the following construction:
%e {1,a(0),a(1),a(1),a(2),a(1),a(2),a(2),a(3),...,a(A000120(n-1)),...}
%e where A000120 = {0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,...}.
%o (PARI) {a(n)=if(n==0,1,1+sum(k=0,n-1, binomial(n,k)*a(subst(Pol(binary(n-k-1)),x,1))))}
%Y Cf. A101910, A000120.
%K eigen,nonn
%O 0,2
%A _Paul D. Hanna_, Dec 21 2004