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A006348
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a(n) = (n+2)*a(n-1) + (-1)^n.
(Formerly M3609)
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0
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0, 1, 4, 25, 174, 1393, 12536, 125361, 1378970, 16547641, 215119332, 3011670649, 45175059734, 722800955745, 12287616247664, 221177092457953, 4202364756701106
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n) is a function of the subfactorials... a(n)= A000166(n+2)-1/3*(n+2)! /Q ie... 1= 9-24/3, 4= 44-120/3, 25=265-720/3... [From Gary Detlefs (gdetlefs(AT)aol.com), Dec 17 2009]
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| a(n)=(n+1)(a(n-1)+a(n-2)) [From Gary Detlefs (gdetlefs(AT)aol.com), Dec 17 2009]
E.g.f. with offset 0: ((2+3*x+x^3)*exp(-x)-2)/(1-x)^4. From int(((9+8*x+6*x^2+x^4)*exp(-x)-8)/(1-x)^5, x) with input 0 for x=0. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), May 03 2010]
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MAPLE
| a:=n->n!*sum((-1)^k/k!, k=4..n): seq(a(n), n=3..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 25 2007
a(n) := n-> floor(((n+2)!+1)/E) -(n+2)!/3 [From Gary Detlefs (gdetlefs(AT)aol.com), Dec 17 2009]
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CROSSREFS
| Sequence in context: A034494 A084210 A093683 * A051820 A166697 A054368
Adjacent sequences: A006345 A006346 A006347 * A006349 A006350 A006351
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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