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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A185308 a(0)=0, a(1)=0; for n>1, a(n) = a(n-1) + n*a(n-2) + 1. 5
 0, 0, 1, 2, 7, 18, 61, 188, 677, 2370, 9141, 35212, 144905, 602662, 2631333, 11671264, 53772593, 252184082, 1220090757, 6011588316, 30413403457, 156656758094, 825751634149, 4428857070312, 24246896289889, 134968323047690, 765387626584805, 4409532348872436 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA a(0)=a(1)=0, a(2)=1, a(n) = 2*a(n-1)+(n-1)*a(n-2)-(n-1)*a(n-3). - Vincenzo Librandi, Dec 24 2012 a(n) ~ (sqrt(Pi)-sqrt(2))/2 * n^(n/2+1/2)*exp(sqrt(n)-n/2-1/4) * (1+19/(24*sqrt(n))). - Vaclav Kotesovec, Dec 26 2012 E.g.f.: 1/2*exp(x)*(exp(x^2/2)*(x+1)*(sqrt(2*Pi)*erf(x/sqrt(2))-2)+2). - Vaclav Kotesovec, Dec 27 2012 MATHEMATICA RecurrenceTable[{a[0] == 0, a[1] == 0, a[n] == a[n - 1] + n a[n - 2] + 1}, a, {n, 0, 30}] (* Bruno Berselli, Dec 24 2012 *) FullSimplify[CoefficientList[Series[1/2*E^x*(E^(x^2/2)*(x+1)*(Sqrt[2*Pi]*Erf[x/Sqrt[2]]-2)+2), {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Dec 27 2012 *) PROG (Magma) I:=[0, 0, 1, 2]; [n le 4 select I[n] else 2*Self(n-1)+(n-2)*Self(n-2)-(n-2)*Self(n-3): n in [1..30]]; Vincenzo Librandi, Dec 24 2012 CROSSREFS Sequence in context: A214836 A176813 A000988 * A002214 A303742 A340738 Adjacent sequences: A185305 A185306 A185307 * A185309 A185310 A185311 KEYWORD nonn AUTHOR Olivier Gérard, Nov 02 2012 EXTENSIONS More terms from Vincenzo Librandi, Dec 24 2012 Edited by Bruno Berselli, Dec 24 2012 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 September 7 22:13 EDT 2024. Contains 375749 sequences. (Running on oeis4.)