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A033540 a(n+1) = n*(a(n)+1) for n >= 1, a(1) = 1. 7
1, 2, 6, 21, 88, 445, 2676, 18739, 149920, 1349289, 13492900, 148421911, 1781062944, 23153818285, 324153456004, 4862301840075, 77796829441216, 1322546100500689, 23805829809012420, 452310766371235999 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

FORMULA

a(n) = n!*(1+1/0!+1/1!+...+1/(n-1)!). - Jon Bentley, jlb(AT)research.bell-labs.com

For n>=1, a(n+1) = floor((1+e)*n!)-1. - Benoit Cloitre, Sep 07 2002

a(n) = n! + A007526(n). E.g.f.: (1+x*exp(x))/(1-x). - Vladeta Jovovic, Feb 02 2003

a(n) = (n+1)*a(n-1)-(2*n-3)*a(n-2)+(n-3)*a(n-3) for n>=4. - Jaume Oliver Lafont, Sep 11 2009

a(n) = n! + floor(e*n!)-1, n>0. - Gary Detlefs, Jun 06 2010

MATHEMATICA

a=1; lst={a}; Do[a=a*n+n; AppendTo[lst, a], {n, 1, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 25 2008 *)

FoldList[#1*#2 + #2 &, 1, Range[19]] (* Robert G. Wilson v, Jul 07 2012 *)

nxt[{a_, n_}]:={n(a+1), n+1}; Transpose[NestList[nxt, {1, 1}, 20]][[1]] (* Harvey P. Dale, Jun 20 2014 *)

PROG

(MAGMA) I:=[1, 2, 6]; [n le 3 select I[n] else (n+1)*Self(n-1)-(2*n-3)*Self(n-2)+(n-3)*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 21 2014

CROSSREFS

Sequence in context: A150227 A263852 A189243 * A177479 A147719 A231166

Adjacent sequences:  A033537 A033538 A033539 * A033541 A033542 A033543

KEYWORD

nonn,easy

AUTHOR

Antti Karttunen

STATUS

approved

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Last modified October 13 18:57 EDT 2019. Contains 327981 sequences. (Running on oeis4.)