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A050352
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Number of 4-level labeled linear rooted trees with n leaves.
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5
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1, 1, 7, 73, 1015, 17641, 367927, 8952553, 248956855, 7788499561, 270732878647, 10351919533033, 431806658432695, 19512813265643881, 949587798053709367, 49512355251796513513, 2753726282896986372535, 162725978752448205162601
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Index entries for sequences related to rooted trees
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FORMULA
| E.g.f.: (3-2*e^x)/(4-3*e^x).
a(n) is asymptotic to (1/12)*n!/log(4/3)^(n+1). - Benoit Cloitre, Jan 30 2003
For m-level trees (m>1), e.g.f. is (m-1-(m-2)*e^x)/(m-(m-1)*e^x) and number of trees is 1/(m*(m-1))*sum(k>=0, (1-1/m)^k*k^n). Here m=4, so a(n)=(1/12)*sum(k>=0, (3/4)^k*k^n) (for n>0). - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 30 2003
Let f(x) = (1+x)*(1+2*x). Let D be the operator g(x) -> d/dx(f(x)*g(x)). Then for n>=1, a(n) = D^(n-1)(1) evaluated at x = 1. Compare with the result A000670(n) = D^(n-1)(1) at x = 0. See also A194649. - Peter Bala, Sept 05 2011
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PROG
| (PARI) a(n)=n!*if(n<0, 0, polcoeff((3-2*exp(x))/(4-3*exp(x))+O(x^(n+1)), n))
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CROSSREFS
| Cf. A000670, A050351-A050359.
Equals 1/3 * A032033(n) for n>0.
Sequence in context: A114429 A124547 A084363 * A112939 A058350 A048174
Adjacent sequences: A050349 A050350 A050351 * A050353 A050354 A050355
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KEYWORD
| nonn
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), Oct 15 1999.
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