

A093858


a(0) = 1, a(1)= 2, a(n) = (a(n+1)  a(n1))/n, or a(n+1) = n*a(n) + a(n1).


3



1, 2, 3, 8, 27, 116, 607, 3758, 26913, 219062, 1998471, 20203772, 224239963, 2711083328, 35468323227, 499267608506, 7524482450817, 120890986821578, 2062671258417643, 37248973638339152, 709793170386861531
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OFFSET

0,2


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200


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, Sep 14 2005
E.g.f.: 3*Pi*(BesselI(1, 2)*BesselY(0, 2*I*sqrt(1x)) + I*BesselY(1, 2*I)*BesselI(0, 2*sqrt(1x))). Such e.g.f. computations were the result of an email exchange with Gary Detlefs. After differentiation and setting x=0 one has to use simplifications. See the AbramowitzStegun handbook, p. 360, 9.1.16 and p. 375, 9.63.  Wolfdieter Lang, May 19 2010
Lim_{n>infinity} a(n)/(n1)! = 2*BesselI(0,2)  BesselI(1,2) = 6.1498074593094635982566633...  Vaclav Kotesovec, Jan 05 2013


MATHEMATICA

a = 1; b = 2; Print[a]; Print[b]; Do[c = n*b + a; Print[c]; a = b; b = c, {n, 1, 30}] (* Ryan Propper, Sep 14 2005 *)


CROSSREFS

Similar recurrences: A001040, A001053, A058279, A058307.  Wolfdieter Lang, May 19 2010
Sequence in context: A086613 A121401 A318895 * A080568 A091339 A006277
Adjacent sequences: A093855 A093856 A093857 * A093859 A093860 A093861


KEYWORD

easy,nonn


AUTHOR

Amarnath Murthy, Apr 19 2004


EXTENSIONS

a(10)a(20) from Ryan Propper, Sep 14 2005


STATUS

approved



