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A055596
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Expansion of (2-x-2/e^x)/(1-x).
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2
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1, 0, 2, 6, 32, 190, 1332, 10654, 95888, 958878, 10547660, 126571918, 1645434936, 23036089102, 345541336532, 5528661384510, 93987243536672, 1691770383660094, 32143637289541788, 642872745790835758
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| It appears that a(n) = n*a(n-1) + 2(-1)^(n+1) and that the n-th term of any sequence of the form {A(0) =a, A(1)= b, A(n) = (n-1)(A(n-1)+A(n-2))} is A(n) = b*A000166(n) + a*A055596(n). A(n) can also be expressed as A(n) = n*A(n-1) + (2a-b)(-1)^(n+1) [From Gary Detlefs (gdetlefs(AT)aol.com), Jun 13 2009]
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FORMULA
| E.g.f.: (2-x-2exp(-x))/(1-x).
a(n) = (n-1)[ a(n-1) + a(n-2) ], n>2.
a(n)=-n!*[1+2*Sum_{k=1..n}{(-1)^k/k!}], with n>=1 [From Paolo P. Lava (paoloplava(AT)gmail.com), Apr 26 2010]
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PROG
| (PARI) a(n)=if(n<2, n>0, n*a(n-1)-2*(-1)^n)
(PARI) a(n)=if(n<1, 0, n!*polcoeff((2-x-2*exp(-x+x*O(x^n)))/(1-x), n))
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CROSSREFS
| a(n) = n!-2 A000166(n), n>0.
Sequence in context: A092199 A108485 A018940 * A109572 A011820 A206300
Adjacent sequences: A055593 A055594 A055595 * A055597 A055598 A055599
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KEYWORD
| nonn
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AUTHOR
| Gary Detlefs (gdetlefs(AT)absolute-net.com), Jul 10 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 11 2000
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