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The Shift-Moebius transform of powers of 2.
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%I #4 Mar 30 2012 18:37:44

%S 1,1,2,5,12,25,57,115,240,484,996,1987,4041,8071,16252,32527,65292,

%T 130558,261651,523271,1047533,2095138,4192255,8384449,16773161,

%U 33546227,67100496,134201373,268419000,536837755,1073709065,2147417864

%N The Shift-Moebius transform of powers of 2.

%C See triangle A117165 for the definition of the Shift-Moebius transform.

%F a(n) = Sum_{k=1,n} A117165(n,k)*2^(k-1).

%o (PARI) {a(n)=sum(k=1,n,prod(i=0,n, matrix(n,n,r,c,if(r>=c,if((r+n-i)%(c+n-i)==0,moebius((r+n-i)/(c+n-i)),0))))[ n,k]*2^(k-1))}

%Y Cf. A117165, A117175.

%K nonn

%O 1,3

%A _Wouter Meeussen_ and _Paul D. Hanna_, Mar 05 2006