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A132052
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Seventh column of triangle A035342.
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1
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1, 84, 4662, 220500, 9740115, 419625360, 18048090060, 785470565880, 34872721208325, 1587323312675100, 74301594199682850, 3583275362669702700, 178220792065162821975, 9146316814629741747000, 484394828691800237211000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 7,2
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COMMENTS
| a(n), n>=7, enumerates unordered forests composed of seven plane increasing ternary trees with n vertices. See A001147 (number of increasing ternary trees) and a D. Callan comment there. For a picture of some ternary trees see a W. Lang link under A001764.
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FORMULA
| E.g.f. ((x*c(x/2)*(1-2*x)^(-1/2))^7)/7!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0.
E.g.f. (-1+(1-2*x)^(-1/2))^7/7!.
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EXAMPLE
| a(8)=84=3*binomial(8,2) increasing ternary 7-forest with n=8 vertices: there are three 7-forests (six one vertex trees together with any of the three different 2-vertex trees) each with binomial(8,2)= 28 increasing labelings.
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CROSSREFS
| Cf. A132051 (sixth column).
Sequence in context: A004379 A075906 A075909 * A097840 A202923 A145495
Adjacent sequences: A132049 A132050 A132051 * A132053 A132054 A132055
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Sep 14 2007
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