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A007715
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Number of 5-leaf rooted trees with n levels.
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1
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1, 7, 27, 75, 170, 336, 602, 1002, 1575, 2365, 3421, 4797, 6552, 8750, 11460, 14756, 18717, 23427, 28975, 35455, 42966, 51612, 61502, 72750, 85475, 99801, 115857, 133777, 153700, 175770, 200136, 226952, 256377, 288575, 323715, 361971, 403522
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Huberman, B. A.; Hogg, T.; Complexity and adaptation. Evolution, games and learning (Los Alamos, N.M., 1985). Phys. D 22 (1986), no. 1-3, 376-384.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..5000
Index entries for sequences related to rooted trees
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FORMULA
| Expansion of (1+2x+2x^2)/(1-x)^5.
a(n)=n*(n+1)*(5*n^2+n+6)/24 - T. D. Noe, Feb 09 2007
a(0)=1, a(1)=7, a(2)=27, a(3)=75, a(4)=170, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5) [From Harvey P. Dale, Jul 20 2011]
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MATHEMATICA
| Table[n(n+1)(5n^2+n+6)/24, {n, 40}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {1, 7, 27, 75, 170}, 40] (* From Harvey P. Dale, Jul 20 2011 *)
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PROG
| (MAGMA) [n*(n+1)*(5*n^2+n+6)/24: n in [1..45]]; // Vincenzo Librandi, Jul 21 2011
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CROSSREFS
| Sequence in context: A159065 A098931 A143690 * A161439 A039623 A162210
Adjacent sequences: A007712 A007713 A007714 * A007716 A007717 A007718
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KEYWORD
| easy,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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