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A001120
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a(1) = 1; for n > 1, a(n) = n*a(n-1) + (-1)^n.
(Formerly M2760 N1110)
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3
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1, 3, 8, 33, 164, 985, 6894, 55153, 496376, 4963761, 54601370, 655216441, 8517813732, 119249392249, 1788740883734, 28619854139745, 486537520375664, 8757675366761953, 166395831968477106, 3327916639369542121
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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).
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FORMULA
| Nearest integer to n!(1+1/e).
a(n) = A000166(n) + n! . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 04 2005
a(n)=n!*(1+Sum{k=0..n}{(-1)^k/k!}, with n>=1 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 21 2008]
a(n)=(n-1)*(a(n-1)+a(n-2)), n>2 [From Gary Detlefs (gdetlefs(AT)aol.com), Apr 11 2010]
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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))
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CROSSREFS
| A000166 has a similar recurrence.
Sequence in context: A195499 A109655 A184255 * A117722 A024419 A186517
Adjacent sequences: A001117 A001118 A001119 * A001121 A001122 A001123
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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