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A008546
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Quintuple factorial numbers: product[ k=0..n-1 ] (5*k+4).
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20
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1, 4, 36, 504, 9576, 229824, 6664896, 226606464, 8837652096, 388856692224, 19053977918976, 1028914807624704, 60705973649857536, 3885182313590882304, 268077579637770878976, 19837740893195045044224
(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)= 4*A034301(n) = (5*n-1)(!^5), n >= 1, a(0) := 1.
a(n) ~ 2^(1/2)*pi^(1/2)*Gamma(4/5)^-1*n^(3/10)*5^n*e^-n*n^n*{1 + 1/300*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001
G.f.: 1/(1-4x/(1-5x/(1-9x/(1-10x/(1-14x/(1-15x/(1-19x/(1-20x/(1-24x/(1-... (continued fraction). - DELEHAM Philippe, Jan 08 2012
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MAPLE
| f := n->product( (5*k-1), k=0..n);
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MATHEMATICA
| s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 3, 5!, 5}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 08 2008]
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CROSSREFS
| a(n)= A011801(n+1, 1) (first column of triangle). Cf. A008548, A047056, A047055, A052562, A051150, A052562.
Sequence in context: A002690 A094417 A138435 * A024253 A052746 A145084
Adjacent sequences: A008543 A008544 A008545 * A008547 A008548 A008549
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KEYWORD
| nonn
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AUTHOR
| Joe Keane (jgk(AT)jgk.org)
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