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Search: id:A084261
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| A084261 |
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A binomial transform of factorial numbers. |
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+0
8
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| 1, 1, 2, 4, 9, 21, 52, 134, 361, 1009, 2926, 8768, 27121, 86373, 282864, 950866, 3277169, 11564353, 41739130, 153919324, 579411641, 2224535125, 8703993420, 34681783422, 140637608089, 580019801201, 2431509498406, 10355296410712
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Binomial transform of A000142 (with interpolated zeros).
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FORMULA
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a(n)=sum{k=0..floor(n/2), C(n, 2k)k! }; a(n)=sum{k=0..n, C(n, k)(k/2)!(1+(-1)^k)/2 }.
E.g.f.: exp(x)*(1+sqrt(Pi)/2*x*exp(x^2/4)*erf(x/2)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 25 2003
O.g.f.: A(x) = 1/(1-x-x^2/(1-x-x^2/(1-x-2*x^2/(1-x-2*x^2/(1-x-3*x^2/(1-... -x-[(n+1)/2]*x^2/(1- ...))))))) (continued fraction). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 17 2006
a_n ~ (1/2) * sqrt(Pi*n/e)*(n/2)^(n/2)*exp(-n/2 + sqrt(2n)). - Cecil C Rousseau (ccrousse(AT)memphis.edu), Mar 14 2006: (cf. A002896).
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CROSSREFS
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Sequence in context: A148071 A000636 A136753 this_sequence A063026 A106219 A032129
Adjacent sequences: A084258 A084259 A084260 this_sequence A084262 A084263 A084264
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 26 2003
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