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<DIV>Seqfans, <BR> Just
found an o.g.f. for A014070(n) = C(2^n,n): </DIV>
<DIV> </DIV>
<DIV>(1) G.f.: A(x) = Sum_{n>=0} log(1 + 2^n*x)^n / n!.</DIV>
<DIV> </DIV>
<DIV>More generally, we have the nontrivial identity: </DIV>
<DIV> </DIV>
<DIV>(2) Sum_{n>=0} log(1 + q^n*x)^n/n! = Sum_{n>=0}
C(q^n,n)*x^n. </DIV>
<DIV> </DIV>
<DIV>The proof is easy given the following formula for A008275, </DIV>
<DIV>the Stirling numbers of the first kind: </DIV>
<DIV> E.g.f. for k-th column of A008275 is ln(1+x)^k/k!. </DIV>
<DIV> </DIV>
<DIV>My questions: </DIV>
<DIV>Can any other interesting result be derived from (2)? </DIV>
<DIV>Thanks, </DIV>
<DIV> Paul </DIV></BODY></HTML>