A085923 a(0) = 1, a(n+1) = (n+1)*(a(n) + n).

1, 1, 4, 18, 84, 440, 2670, 18732, 149912, 1349280, 13492890, 148421900, 1781062932, 23153818272, 324153455990, 4862301840060, 77796829441200, 1322546100500672, 23805829809012402, 452310766371235980, 9046215327424719980, 189970521875919120000, 4179351481270220640462

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

From Vaclav Kotesovec, Oct 21 2012: (Start)

E.g.f.: (1+exp(x)*x^2)/(1-x).

Recurrence: (n-2)*a(n) = (n-1)*n*a(n-1) - (n-1)*n*a(n-2).

a(n) ~ n!*(1+e).

(End)

a(n) = n!*(1+Sum_{k=0..n-2} 1/k!), for n>1. - Vaclav Kotesovec, Oct 28 2012

Mathematica

a=1; Table[a=(a+n)*(n+1), {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Nov 20 2009 *)
Rest[CoefficientList[Series[-(1+E^x*x^2)/(x-1), {x, 0, 20}], x]*Range[0, 20]!] (* Vaclav Kotesovec, Oct 21 2012 *)
Flatten[{1, Table[n!*(1+Sum[1/k!, {k, 0, n-2}]), {n, 2, 20}]}] (* Vaclav Kotesovec, Oct 28 2012 *)
nxt[{n_, a_}]:={n+1, (n+1)(a+n)}; NestList[nxt, {0, 1}, 30][[;; , 2]] (* Harvey P. Dale, Apr 16 2024 *)

Prog

(PARI) x='x+O('x^66); Vec(serlaplace((1+exp(x)*x^2)/(1-x))) \\ Joerg Arndt, May 10 2013
(PARI) a(n)=if(n==0, 1, n*(a(n-1) + n-1) ); \\ Joerg Arndt, May 11 2013

Crossrefs

Sequence in context: A010849 A007859 A185132 * A110166 A046885 A247637

Adjacent sequences: A085920 A085921 A085922 * A085924 A085925 A085926

Keyword

nonn,changed

Author

Amarnath Murthy, Jul 12 2003

Extensions

More terms from Ray Chandler, Sep 13 2003

Corrected offset, Joerg Arndt, May 10 2013

Status

approved