A085110 a(1)=1, then add 1 multiply by 2 to get a(2), subtract 1 and multiply by 3 to get a(3), add 1 and multiply by 4 to get a(4) and so on.

1, 4, 9, 40, 195, 1176, 8225, 65808, 592263, 5922640, 65149029, 781788360, 10163248667, 142285481352, 2134282220265, 34148515524256, 580524763912335, 10449445750422048, 198539469258018893, 3970789385160377880, 83386577088367935459, 1834504695944094580120

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..372

Formula

a(1)=1, a(n)=n*a(n-1)+(-1)^n*n ; a(n)=round(n!*(2-exp(-1)))+(-1)^n. - Benoit Cloitre, Sep 24 2006

E.g.f.: t*(exp(-t)-2)/(t-1). - Robert Israel, Aug 04 2014

a(n) = ((n-2)*n/(n-1))*a(n-1) + n*a(n-2). - Robert Israel, Aug 04 2014

Maple

a[1]:= 1:
for n from 2 to 30 do a[n]:= n*(a[n-1]+(-1)^n) od:
seq(a(n), n=1..30); # Robert Israel, Aug 04 2014

Mathematica

nxt[{n_, a_}]:={n+1, If[OddQ[n], (n+1)(a+1), (n+1)(a-1)]}; Transpose[ NestList[ nxt, {1, 1}, 30]][[2]] (* Harvey P. Dale, Aug 04 2014 *)

Prog

(PARI) a(n)=if(n<2, 1, n*a(n-1)+(-1)^n*n) \\ Benoit Cloitre, Sep 24 2006

Crossrefs

Sequence in context: A370602 A354738 A073414 * A013459 A041229 A042887

Adjacent sequences: A085107 A085108 A085109 * A085111 A085112 A085113

Keyword

nonn

Author

Amarnath Murthy, Jul 04 2003

Extensions

More terms from Sam Alexander, Feb 26 2004

Corrected and extended by Harvey P. Dale, Aug 04 2014

Status

approved