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A001120 a(1) = 1; for n > 1, a(n) = n*a(n-1) + (-1)^n.
(Formerly M2760 N1110)
5
1, 3, 8, 33, 164, 985, 6894, 55153, 496376, 4963761, 54601370, 655216441, 8517813732, 119249392249, 1788740883734, 28619854139745, 486537520375664, 8757675366761953, 166395831968477106, 3327916639369542121, 69886249426760384540, 1537497487388728459881 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..100

J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]

FORMULA

Nearest integer to n!(1+1/e).

a(n) = A000166(n) + n!. - Philippe Deléham, Sep 04 2005

a(n) = n!*(1+Sum_{k=0..n} (-1)^k/k!, n>=1. - Paolo P. Lava, Nov 21 2008

a(n) = (n-1)*(a(n-1)+a(n-2)), n>2. - Gary Detlefs, Apr 11 2010

MATHEMATICA

t = {1}; Do[AppendTo[t, n*t[[-1]] + (-1)^n], {n, 2, 20}]; t (* T. D. Noe, Jun 26 2012 *)

RecurrenceTable[{a[1]==1, a[n]==n a[n-1]+(-1)^n}, a, {n, 30}] (* Harvey P. Dale, Feb 19 2018 *)

PROG

(PARI) a(n)=if(n<2, n>0, n*a(n-1)+(-1)^n)

(PARI) a(n)=if(n<1, 0, n!*polcoeff((1+exp(-x+x*O(x^n)))/(1-x), n))

CROSSREFS

A000166 has a similar recurrence.

Sequence in context: A225688 A109655 A184255 * A302629 A322303 A117722

Adjacent sequences:  A001117 A001118 A001119 * A001121 A001122 A001123

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Simon Plouffe

STATUS

approved

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Last modified April 19 09:21 EDT 2019. Contains 322241 sequences. (Running on oeis4.)