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A008543
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Sextuple factorial numbers: product[ k=0..n-1 ] (6*k+5).
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21
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1, 5, 55, 935, 21505, 623645, 21827575, 894930575, 42061737025, 2229272062325, 131527051677175, 8549258359016375, 606997343490162625, 46738795448742522125, 3879320022245629336375, 345259481979861010937375
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
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FORMULA
| a(n)= 5*A034787(n) = (6*n-1)(!^6), n >= 1, a(0) := 1.
E.g.f. (1-6*x)^(-5/6).
a(n) ~ 2^(1/2)*pi^(1/2)*Gamma(5/6)^-1*n^(1/3)*6^n*e^-n*n^n*{1 + 1/72*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001
G.f.: 1/(1-5x/(1-6x/(1-11x/(1-12x/(1-17x/(1-18x/(1-23x/(1-24x/(1-... (continued fraction). - DELEHAM Philippe, Jan 08 2012
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MAPLE
| f := n->product( (6*k-1), k=0..n);
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MATHEMATICA
| s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 4, 5!, 6}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 08 2008]
FoldList[Times, 1, 6Range[0, 15]+5] (* From Harvey P. Dale, Feb 20 2011 *)
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PROG
| (PARI) a(n)=prod(k=1, n, 6*k-1) \\ Charles R Greathouse IV, Aug 17 2011
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CROSSREFS
| a(n)= A013988(n+1, 1) (first column of triangle). Cf. A004994, A049308, A047058, A051151.
Sequence in context: A132865 A145662 A094418 * A057130 A141357 A093352
Adjacent sequences: A008540 A008541 A008542 * A008544 A008545 A008546
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KEYWORD
| nonn,easy
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AUTHOR
| Joe Keane (jgk(AT)jgk.org)
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