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<DIV> <BR>> Limit[Log[10, Hypergeometric2F1[(1/2)*(1 - n), (-(1/2))*n,
2, 4]]/n, n -> Infinity]<BR>> <A
href="http://www.research.att.com/projects/OEIS?Anum=A114473">http://www.research.att.com/projects/OEIS?Anum=A114473</A><BR>>
0.47712...</DIV>
<DIV> </DIV>
<DIV>Limit[a(n)/10^n,n->Infinity] = Log[10, 3 ] <BR>=
0.477121254719662437295027903...<BR> </DIV>
<DIV>
<DIV>since the real root possessing the smallest absolute value
</DIV>
<DIV>of expression (1-2*x-3*x^2) (found in the g.f.) equals
1/3.</DIV>
<DIV> <BR>> Limit[Log[10, Hypergeometric2F1[-n + 1, n + 2, 2, -1]]/n, n
-> Infinity]<BR>> Limit[Log[10, Hypergeometric2F1[-n + 1, n + 1, 1,
-1]]/n, n -> Infinity]<BR>> <A
href="http://www.research.att.com/projects/OEIS?Anum=A114470">http://www.research.att.com/projects/OEIS?Anum=A114470</A><BR>>
<A
href="http://www.research.att.com/projects/OEIS?Anum=A114472">http://www.research.att.com/projects/OEIS?Anum=A114472</A><BR>>
0.76555...<BR>> <BR> </DIV></DIV>
<DIV>Limit[a(n)/10^n,n->Infinity] = Log[10, 3+2*sqrt(2) ] <BR>=
0.765551370675726156638799048...<BR> </DIV>
<DIV>since the real root possessing the
smallest absolute value </DIV>
<DIV>of expression (1-6*x+x^2) (found in the g.f.) equals
1/(3+2*sqrt(2)).</DIV>
<DIV> </DIV>
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