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A016109
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Expansion of 1/((1-7x)(1-8x)(1-9x)(1-10x)).
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0
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1, 34, 725, 12410, 186501, 2571114, 33339685, 413066170, 4941549701, 57504755594, 654463491045, 7314256515930, 80522026412101, 875355238834474, 9415203971344805, 100355146006589690
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (34,-431,2414,-5040).
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FORMULA
| If we define f(m,j,x)=sum(binomial(m,k) *stirling2(k,j) *x^(m-k), k=j..m) then a(n-3)=f(n,3,7), (n>=3). [From Milan R. Janjic (agnus(AT)blic.net), Apr 26 2009]
a(n) = 19*a(n-1) - 90*a(n-2) + 8^(n+1) - 7^(n+1), n>=2. - Vincenzo Librandi, Mar 12 2011
a(n) = (10^(n+3)-3*9^(n+3)+3*8^(n+3)-7^(n+3))/6. - Bruno Berselli, Mar 12 2011
a(0)=1, a(1)=34, a(2)=725, a(3)=12410, a(n)=34*a(n-1)-431*a(n-2)+ 2414*a(n-3)-5040*a(n-4) [From Harvey P. Dale, Jan 26 2012]
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MATHEMATICA
| CoefficientList[Series[1/((1-7x)(1-8x)(1-9x)(1-10x)), {x, 0, 20}], x] (* or *) LinearRecurrence[{34, -431, 2414, -5040}, {1, 34, 725, 12410}, 21] (* From Harvey P. Dale, Jan 26 2012 *)
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CROSSREFS
| Sequence in context: A061689 A166217 A188711 * A028211 A028207 A028193
Adjacent sequences: A016106 A016107 A016108 * A016110 A016111 A016112
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
| Offset changed to 0 by Vincenzo Librandi, Janjic formula adapted, Mar 12 2011
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