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A005442
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a(n) = n!*Fibonacci(n+1) (cf. A000045).
(Formerly M3549)
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8
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1, 1, 4, 18, 120, 960, 9360, 105840, 1370880, 19958400, 322963200, 5748019200, 111607372800, 2347586841600, 53178757632000, 1290674601216000, 33413695451136000, 919096314200064000, 26768324463648768000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of ways to use the elements of {1,..,n} once each to form a sequence of lists, each having length 1 or 2. - Bob Proctor, Apr 18 2005
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REFERENCES
| P. R. J. Asveld, Fibonacci-like differential equations with a polynomial nonhomogeneous term, Fib. Quart. 27 (1989), 303-309.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 494
Index entries for related partition-counting sequences
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FORMULA
| a(n)= A039948(n, 0). E.g.f.: 1/(1-x-x^2).
a(n) = n*a(n-1)+n*(n-1)*a(n-2). - Detlef Pauly (dettodet(AT)yahoo.de), Sep 22 2003
a(n) = D^n(1/(1-x)) evaluated at x = 0, where D is the operator sqrt(1+4*x)*d/dx. Cf. A080599 and A052585. - Peter Bala, Dec 07 2011
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MATHEMATICA
| Table[Fibonacci[n + 1]*n!, {n, 0, 20}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 09 2009]
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CROSSREFS
| Row sums of Fibonacci Jabotinsky-triangle A039692. A080599 and A052585.
Sequence in context: A137567 A162224 A053529 * A084661 A112294 A073511
Adjacent sequences: A005439 A005440 A005441 * A005443 A005444 A005445
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KEYWORD
| nonn
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AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| Comments from Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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