The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A058279 a(0)=a(1)=1, a(n)=a(n-2)+(n+1)*a(n-1). 7
 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; text; internal format)
 OFFSET 0,3 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 C. Cannings, The Stationary Distributions of a Class of Markov Chains, Applied Mathematics, Vol. 4 No. 5, 2013, pp. 769-773. FORMULA a(n) is asymptotic to c*n! with c=0.9007... - Benoit Cloitre, Sep 03 2002 Right asymptotic (with offset=0) is a(n) ~ c * (n+1)!, where c = 2*BesselI(1,2)-BesselI(0,2) = 0.9016884069385908593273044... - Vaclav Kotesovec, Jan 05 2013 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. [Wolfdieter Lang, May 19 2010] MAPLE A058279 := proc(n) option remember; if n <= 1 then 1 else A058279(n-2)+(n+1)*A058279(n-1); fi; end; MATHEMATICA RecurrenceTable[{a[0] == a[1] == 1, a[n] == a[n-2] + a[n-1] (n+1)}, a, {n, 30}] (* Vincenzo Librandi, May 06 2013 *) PROG (Magma) [n le 2 select 1 else Self(n-2)+Self(n-1)*(n): n in [1..30]]; // Vincenzo Librandi, May 06 2013 CROSSREFS See A058307 for the same recurrence with 0,1 inputs. [Wolfdieter Lang, May 19 2010] Sequence in context: A354308 A357617 A350474 * A143405 A303793 A141154 Adjacent sequences: A058276 A058277 A058278 * A058280 A058281 A058282 KEYWORD nonn AUTHOR N. J. A. Sloane, Dec 09 2000 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 28 20:13 EST 2022. Contains 358421 sequences. (Running on oeis4.)