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A093858
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a(0) = 1, a(1)= 2, a(n) = {a(n+1)-a(n-1)}/n, or a(n+1) = n*a(n) +a(n-1).
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2
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1, 2, 3, 8, 27, 116, 607, 3758, 26913, 219062, 1998471, 20203772, 224239963, 2711083328, 35468323227, 499267608506, 7524482450817, 120890986821578, 2062671258417643, 37248973638339152, 709793170386861531
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n) = -2*(BesselI[n, -2]*(2 BesselK[0, 2] - BesselK[1, 2]) + (-2 BesselI[0, 2] + BesselI[1, -2])*BesselK[n, 2]) - Ryan Propper (rpropper(AT)stanford.edu), Sep 14 2005
E.g.f.: -3*Pi*(BesselI(1, 2)*BesselY(0, 2*I*sqrt(1-x)) + I*BesselY(1, 2*I)*BesselI(0, 2*sqrt(1-x))). Such e.g.f. computations were the result of an 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 and p.375, 9.63. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), May 19 2010]
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EXAMPLE
| Similiar recurrences: A001040, A001053, A058279, A058307. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), May 19 2010]
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MATHEMATICA
| a = 1; b = 2; Print[a]; Print[b]; Do[c = n*b + a; Print[c]; a = b; b = c, {n, 1, 30}] (Propper)
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CROSSREFS
| Sequence in context: A041503 A086613 A121401 * A080568 A091339 A006277
Adjacent sequences: A093855 A093856 A093857 * A093859 A093860 A093861
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KEYWORD
| easy,nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 19 2004
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EXTENSIONS
| More terms from Ryan Propper (rpropper(AT)stanford.edu), Sep 14 2005
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