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A052316
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Number of labeled rooted trees with n nodes and 2-colored internal (non-leaf) nodes.
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3
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1, 4, 30, 344, 5370, 106452, 2562182, 72592816, 2367054450, 87320153900, 3595646533182, 163492924997448, 8136172620013802, 439858024910227588, 25670670464821310070, 1608575860476990991712, 107716675117341985862370
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| N. J. A. Sloane, Transforms
Index entries for sequences related to rooted trees
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FORMULA
| Divides by 2n and shifts left under exponential transform.
E.g.f.: -x-LambertW(-2*x*exp(-x)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 17 2003
a(n)=sum(j=1..n, j^(n-1)*2^j*(-1)^(n-j)*binomial(n,j)), n>1, a(1)=1. [From Vladimir Kruchinin, Jan 24 2012]
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PROG
| (Maxima) a(n):=if n=1 then 1 else sum(j^(n-1)*2^j*(-1)^(n-j)*binomial(n, j), j, 1, n); [From Vladimir Kruchinin, Jan 24 2012]
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CROSSREFS
| Cf. A004113, A004114, A052317.
Sequence in context: A121413 A001761 A099712 * A089918 A132622 A118792
Adjacent sequences: A052313 A052314 A052315 * A052317 A052318 A052319
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KEYWORD
| nonn,eigen
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), Dec 15 1999.
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