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A045755
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8-fold factorials: product[k=0..n-1] (8*k+1).
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20
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1, 1, 9, 153, 3825, 126225, 5175225, 253586025, 14454403425, 939536222625, 68586144251625, 5555477684381625, 494437513909964625, 47960438849266568625, 5035846079172989705625, 569050606946547836735625
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n+1) = (8*n+1)(!^8).
a(n) = Sum_{k=0..n} (-8)^(n-k)*A048994(n, k); A048994 = Stirling-1 numbers.
E.g.f. (1-8*x)^(-1/8).
G.f.: 1+x/(1-9x/(1-8x/(1-17x/(1-16x/(1-25x/(1-24x/(1-33x/(1-32x/(1-... (continued fraction). - DELEHAM Philippe, Jan 07 2012
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MAPLE
| f := n->product(8*k+1), k=0..(n-1));
restart: G(x):=(1-8*x)^(-1/8): 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, 8, 5!, 8}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 08 2008]
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PROG
| (PARI) a(n)=if(n==0, 1, prod(k=0, n, 8*k+1))
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CROSSREFS
| Cf. k-fold factorials : A000142, A001147, A007559, A007696, A008548, A008542, A045754.
Cf. A051187, A113135.
Sequence in context: A133309 A151835 A113391 * A009037 A012148 A193540
Adjacent sequences: A045752 A045753 A045754 * A045756 A045757 A045758
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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 14 2008 at the suggestion of Artur Jasinski.
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