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Search: id:A007559
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| A007559 |
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Triple factorial numbers (3*n-2)!!! with leading 1 added.
(Formerly M3627)
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+0
61
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| 1, 1, 4, 28, 280, 3640, 58240, 1106560, 24344320, 608608000, 17041024000, 528271744000, 17961239296000, 664565853952000, 26582634158080000, 1143053268797440000, 52580450364682240000, 2576442067869429760000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) = number of increasing quaternary trees on n vertices. (See A001147 for ternary and A000142 for binary trees.) - David Callan (callan(AT)stat.wisc.edu), Mar 30 2007
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
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FORMULA
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E.g.f.: (1-3*x)^(-1/3).
a(n) ~ 2^(1/2)*pi^(1/2)*Gamma(1/3)^-1*n^(-1/6)*3^n*e^-n*n^n*{1 - 1/36*n^-1 - ...}. - Joe Keane (jgk(AT)jgk.org), Nov 22 2001
a(0) := 1, a(n)=(3*n-2)!!! := product(3*k+1, k=0..n-1).
a(n)= 3^n*Pochhammer(1/3, n).
a(n) = Sum_{k=0..n} (-3)^(n-k)*A048994(n, k) .- Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 29 2005
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CROSSREFS
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Cf. A001147, A004987, A032031, A008544, A051141. a(n)= A035469(n, 1), n >= 1, (first column of triangle A035469(n, m)).
Adjacent sequences: A007556 A007557 A007558 this_sequence A007560 A007561 A007562
Sequence in context: A081917 A128318 A032274 this_sequence A138208 A071212 A090353
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KEYWORD
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nonn,nice,easy
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AUTHOR
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njas.
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EXTENSIONS
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Better description from Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de).
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