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Search: id:A008548
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| A008548 |
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Quintuple factorial numbers: product[ k=0..n-1 ] (5*k+1). |
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35
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| 1, 1, 6, 66, 1056, 22176, 576576, 17873856, 643458816, 26381811456, 1213563326976, 61891729675776, 3465936861843456, 211422148572450816, 13953861805781753856, 990724188210504523776, 75295038303998343806976
(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), n>=1, enumerates increasing sextic (6-ary) trees with n vertices. W. Lang, Sept 14 2007.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..50
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.: (1-5*x)^(-1/5).
a(n) ~ 2^(1/2)*pi^(1/2)*gamma(1/5)^-1*n^(-3/10)*5^n*e^-n*n^n*{1 + 1/300*n^-1 - ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001
a(n) = Sum_{k=0..n} (-5)^(n-k)*A048994(n, k) .- Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 29 2005
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MAPLE
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f := n->product( (5*k+1), k=0..(n-1));
restart: G(x):=(1-5*x)^(-1/5): f[0]:=G(x): for n from 1 to 29 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..16); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 03 2009]
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MATHEMATICA
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s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 5, 5!, 5}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 08 2008]
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CROSSREFS
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Cf. A001147, A007559, A007696, A034687, A034688, A052562, A047055, A051150.
a(n)= A049385(n, 1) (first column of triangle).
Sequence in context: A151832 A133306 A128319 this_sequence A090358 A112942 A113390
Adjacent sequences: A008545 A008546 A008547 this_sequence A008549 A008550 A008551
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Joe Keane (jgk(AT)jgk.org)
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