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A008542
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Sextuple factorial numbers: product[ k=0..n-1 ] (6*k+1).
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28
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1, 1, 7, 91, 1729, 43225, 1339975, 49579075, 2131900225, 104463111025, 5745471106375, 350473737488875, 23481740411754625, 1714167050058087625, 135419196954588922375, 11510631741140058401875
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n), n>=1, enumerates increasing heptic (7-ary) trees with n vertices. W. Lang, Sept 14 2007. See a D. Callan comment on A007559 (number of increasing quarterny trees).
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FORMULA
| E.g.f. (1-6*x)^(-1/6).
a(n) ~ 2^(1/2)*pi^(1/2)*Gamma(1/6)^-1*n^(-1/3)*6^n*e^-n*n^n*{1 + 1/72*n^-1 - ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001
a(n) = Sum_{k=0..n} (-6)^(n-k)*A048994(n, k) .- Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 29 2005
G.f.: 1+x/(1-7x/(1-6x/(1-13x/(1-12x/(1-19x/(1-18x/(1-25x/(1-24x/(1-... (continued fraction). - DELEHAM Philippe, Jan 08 2012
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MAPLE
| f := n->product( (6*k+1), k=0..(n-1));
restart: G(x):=(1-6*x)^(-1/6): 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..15); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 03 2009]
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MATHEMATICA
| s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 6, 5!, 6}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 08 2008]
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PROG
| (PARI) a(n)=prod(k=1, n-1, 6*k+1) \\ Charles R Greathouse IV, Jul 19 2011
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CROSSREFS
| Cf. A034689, A034723, A034724, A034787, A034788, A004993, A047058, A047657, A051151.
Sequence in context: A151833 A113372 A131940 * A121940 A177784 A124557
Adjacent sequences: A008539 A008540 A008541 * A008543 A008544 A008545
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KEYWORD
| nonn
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AUTHOR
| Joe Keane (jgk(AT)jgk.org)
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