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A001120
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a(0) = a(1) = 1; for n > 1, a(n) = n*a(n-1) + (-1)^n.
(Formerly M2760 N1110)
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6
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1, 1, 3, 8, 33, 164, 985, 6894, 55153, 496376, 4963761, 54601370, 655216441, 8517813732, 119249392249, 1788740883734, 28619854139745, 486537520375664, 8757675366761953, 166395831968477106, 3327916639369542121, 69886249426760384540, 1537497487388728459881
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OFFSET
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0,3
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REFERENCES
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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).
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LINKS
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FORMULA
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Nearest integer to n!(1+1/e).
a(n) = (n-1)*(a(n-1)+a(n-2)), n>2. - Gary Detlefs, Apr 11 2010
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MAPLE
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a:= proc(n) option remember;
`if`(n<2, 1, n*a(n-1)+(-1)^n)
end:
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MATHEMATICA
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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 *)
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PROG
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(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))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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