The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A003048 a(n+1) = n*a(n) - (-1)^n. 1
 1, 2, 3, 10, 39, 196, 1175, 8226, 65807, 592264, 5922639, 65149030, 781788359, 10163248668, 142285481351, 2134282220266, 34148515524255, 580524763912336, 10449445750422047, 198539469258018894 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..20. FORMULA E.g.f.: (2-exp(-x))/(1-x) (if offset 0). a(n) = (n-1)! + A002467(n-1), n > 0. (index corrected Mar 07 2022) D-finite with recurrence a(n+2) = n(a(n) + a(n+1)) for n > 0. - Amarnath Murthy, Oct 05 2002 a(n) = 2*(n-1)! - floor(((n-1)! + 1)/e), n > 1. - Gary Detlefs, Apr 11 2010 MAPLE a:= proc(p) option remember; p*a(p-1)-(-1)^p end proc: a(0):= 1: seq(a(p), p=0..19); # Robert Israel, Jan 05 2008 MATHEMATICA a[0] = 1; a[p_] := p*a[p - 1] -(-1)^p; a /@ Range[0, 19] (* Zerinvary Lajos, Mar 29 2007 *) FoldList[#1*#2 - (-1)^#2 &, 1, Range[19]] (* Robert G. Wilson v, Jul 07 2012 *) RecurrenceTable[{a[n + 1] == n a[n] - (-1)^n, a[1] == 1}, a[n], {n, 21}] (* Ray Chandler, Jul 30 2015 *) PROG (PARI) a(n)=if(n<2, n>0, (n-1)*a(n-1)+(-1)^n) (PARI) a(n)=if(n<1, 0, (n-1)!*polcoeff((2-exp(-x+O(x^n)))/(1-x), n-1)) CROSSREFS Cf. A002467. Sequence in context: A141102 A144720 A164933 * A008980 A064183 A050381 Adjacent sequences: A003045 A003046 A003047 * A003049 A003050 A003051 KEYWORD nonn AUTHOR N. J. A. Sloane 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 June 14 02:15 EDT 2024. Contains 373392 sequences. (Running on oeis4.)