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A045754
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7-fold factorials : product[ k=0..n-1] (7*k+1).
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26
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1, 1, 8, 120, 2640, 76560, 2756160, 118514880, 5925744000, 337767408000, 21617114112000, 1534815101952000, 119715577952256000, 10175824125941760000, 936175819586641920000, 92681406139077550080000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Index entries for sequences related to factorial numbers
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FORMULA
| a(n) = Sum_{k=0..n} (-7)^(n-k)*A048994(n, k); where A048994 = Stirling-1 numbers.
E.g.f. (1-7*x)^(-1/7).
G.f.: 1/(1-x/(1-7x/(1-8x/(1-14x/(1-15x/(1-21x/(1-22x/(1-... (continued fraction). - DELEHAM Philippe, Jan 08 2012
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MAPLE
| f := n->product( (7*k+1), k=0..(n-1));
restart: G(x):=(1-7*x)^(-1/7): 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..14); # [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, 0, 5!, 7}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 08 2008]
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PROG
| (PARI) a(n)=prod(k=0, n-1, 7*k+1)
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CROSSREFS
| Cf. k-fold factorials : A000142, A001147, A007559, A007696, A008548, A008542, A045755.
See also A113134.
Unsigned row sums of triangle A051186 (scaled Stirling1).
First column of triangle A132056 (S2(8)).
Cf. A084947, A144739, A144827, A147585, A049209, A051188
Sequence in context: A151834 A007762 A113383 * A173774 A034669 A000848
Adjacent sequences: A045751 A045752 A045753 * A045755 A045756 A045757
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KEYWORD
| nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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EXTENSIONS
| Additional comments from Philippe DELEHAM (kolotoko(AT)wanadoo.fr) and Paul D. Hanna (pauldhanna(AT)juno.com), Oct 29 2005
Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 16 2008 at the suggestion of M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Oct 14 2008
Corrected by Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 03 2009
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