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A058279
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a(0)=a(1)=1, a(n)=a(n-2)+(n+1)*a(n-1).
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5
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1, 1, 4, 17, 89, 551, 3946, 32119, 293017, 2962289, 32878196, 397500641, 5200386529, 73202912047, 1103244067234, 17725107987791, 302430079859681, 5461466545462049, 104070294443638612, 2086867355418234289, 43928284758226558681, 968509132036402525271
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n) is asymptotic to c*n! with c=0.9007... - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 03 2002
E.g.f.: 2*Pi*(I*BesselY(3, 2*I)*BesselI(2, 2*sqrt(1-x)) + BesselI(3, 2)*BesselY(2, 2*I*sqrt(1-x)))/(1-x). Such e.g.f. computations were inspired after e-mail exchange with Gary Detlefs. After differentiation and putting x=0 one has to use simplifications. See the Abramowitz-Stegun handbook, p.360, 9.1.16. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), May 19 2010]
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MAPLE
| A058279 := proc(n) option remember; if n <= 1 then 1 else A058279(n-2)+(n+1)*A058279(n-1); fi; end;
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CROSSREFS
| See A058307 for the same recurrence with 0,1 inputs. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), May 19 2010]
Sequence in context: A110508 A114190 A135168 * A143405 A141154 A112354
Adjacent sequences: A058276 A058277 A058278 * A058280 A058281 A058282
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 09 2000
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