This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A256506 a(n) = (2*n+3)*a(n-1) + a(n-2), a(0)=0, a(1)=1. 1
 0, 1, 7, 64, 711, 9307, 140316, 2394679, 45639217, 960818236, 22144458645, 554572284361, 14995596136392, 435426860239729, 13513228263567991, 446371959557983432, 15636531812792988111, 578998049032898543539, 22596560444095836186132, 927037976256962182174951 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..400 FORMULA a(n) = i*(BesselK[5/2,1]*BesselI[n+5/2,-1] - BesselI[5/2,-1]*BesselK[n+5/2,1]) for n>=0. a(n) = (2/Pi)*(i_{2}^{(1)}(-1)*k_{n+2}(1) - k_{2}(1)*i_{n+2}^{(1)}(-1)) where i_{n}^{(1)}(x) and k_{n}(x) are the modified spherical Bessel functions, n>=0. E.g.f.: sum_{n=0}^{infty} a(n-2) t^{n}/n! = (1/(2 e sqrt(1-2t)))*[(e^2 - 7)*cosh(sqrt(1-2t)) - (e^2 + 7)*sinh(sqrt(1-2t))]. a(n) = (exp(2)-7)*BesselK(5/2 + n, 1)/(exp(1)*sqrt(2*Pi)) - 7*(-1)^n*sqrt(Pi/2) * BesselI(5/2 + n, 1)/exp(1). - Vaclav Kotesovec, Jul 22 2015 a(n) ~ (exp(2)-7) * 2^(n+3/2) * n^(n+2) / exp(n+1). - Vaclav Kotesovec, Jul 22 2015 MATHEMATICA RecurrenceTable[{a[0]==0, a[1]==1, a[n]==a[n-2]+(2n+3)a[n-1]}, a, {n, 20}] PROG (MAGMA) [n le 2 select n-1 else (2*n+1)*Self(n-1)+Self(n-2): n in [1..30]]; // Vincenzo Librandi, May 02 2016 CROSSREFS Sequence in context: A288690 A213515 A293470 * A008787 A261500 A173516 Adjacent sequences:  A256503 A256504 A256505 * A256507 A256508 A256509 KEYWORD easy,nonn AUTHOR G. C. Greubel, Apr 22 2015 EXTENSIONS More terms from Vaclav Kotesovec, Jul 22 2015 STATUS approved

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

Last modified December 8 09:32 EST 2019. Contains 329862 sequences. (Running on oeis4.)