A003048 a(n+1) = n*a(n) - (-1)^n.

1, 2, 3, 10, 39, 196, 1175, 8226, 65807, 592264, 5922639, 65149030, 781788359, 10163248668, 142285481351, 2134282220266, 34148515524255, 580524763912336, 10449445750422047, 198539469258018894

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Crossrefs

Cf. A002467.

Programs

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 *)

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))

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