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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

From Vladeta Jovovic, Feb 02 2003: (Start)

a(n) = n! + A007526(n).

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

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

MAPLE

seq(coeff(series( (1+x*exp(x))/(1-x), x, n+1)*n!, x, n), n = 0..30); # G. C. Greubel, Oct 13 2019

MATHEMATICA

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

(PARI) my(x='x+O('x^30)); Vec(serlaplace( (1+x*exp(x))/(1-x) )) \\ G. C. Greubel, Oct 13 2019

(Sage) [factorial(n)*( (1+x*exp(x))/(1-x) ).series(x, n+1).list()[n] for n in (0..30)] # G. C. Greubel, Oct 13 2019

(GAP) a:=[1, 2, 6];; for n in [4..30] do a[n]:=(n+1)*a[n-1]-(2*n-3)*a[n-2] +(n-3)*a[n-3]; od; a; # G. C. Greubel, Oct 13 2019

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 July 9 19:46 EDT 2020. Contains 335545 sequences. (Running on oeis4.)