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Search: id:A102038
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| A102038 |
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a(n+1) = n*a(n) + a(n-1), a(1)=1 & a(2)=2. |
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+0
3
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| 1, 2, 5, 17, 73, 382, 2365, 16937, 137861, 1257686, 12714721, 141119617, 1706150125, 22321071242, 314201147513, 4735338283937, 76079613690505, 1298088771022522, 23441677492095901, 446689961120844641
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n)=x(n)+y(n) where x(n)/y(n) is the continued fraction [1,2,3,4,...,n].
Using a(n)=x(n)-y(n) instead of a(n)=x(n)+y(n) would give A058307.
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FORMULA
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A102038(n) = A001040(n)+A001053(n) for n>1.
a(n) = Sum_{k=0..n} k!*C([(n+k)/2],k)*C([(n+k+1)/2],k)) = Sum_{k=0..n} k!*A124428(n+k,k). - Paul D. Hanna (pauldhanna(AT)juno.com), Oct 31 2006
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MATHEMATICA
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a[1] = 1; a[2] = 2; a[n_] := a[n] = (n - 1)*a[n - 1] + a[n - 2]; Table[ a[n], {n, 10}] (from Robert G. Wilson v Feb 14 2005)
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PROGRAM
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(PARI) a(n)=sum(k=0, n, k!*binomial((n+k)\2, k)*binomial((n+k+1)\2, k)) - Paul D. Hanna (pauldhanna(AT)juno.com), Oct 31 2006
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CROSSREFS
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Numerators are in A001040 and denominators in A001053.
Cf. A124428.
Sequence in context: A108289 A007779 A084161 this_sequence A002135 A007868 A136726
Adjacent sequences: A102035 A102036 A102037 this_sequence A102039 A102040 A102041
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KEYWORD
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base,easy,nonn
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AUTHOR
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Eric Angelini (eric.angelini(AT)kntv.be), Feb 12 2005
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 14 2005
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