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Search: id:A001040
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| A001040 |
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a(n+1) = n*a(n) + a(n-1).
(Formerly M2863 N1151)
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+0
14
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| 0, 1, 1, 3, 10, 43, 225, 1393, 9976, 81201, 740785, 7489051, 83120346, 1004933203, 13147251985, 185066460993, 2789144166880, 44811373131073, 764582487395121, 13807296146243251, 263103209266016890, 5275871481466581051, 111056404320064218961, 2448516766522879398193
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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If the initial 0 and 1 are omitted, CONTINUANT transform of 1, 2, 3, 4, 5, ...
Numerator of continued fraction given by C(n) = [n; n-1,...,3,2,1]. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 02 2001. Cf. A001053.
Starting (1, 3, 10, 43,...) = eigensequence of triangle A127701 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 29 2008]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
Archimedeans Problems Drive, Eureka, 22 (1959), 15.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
N. J. A. Sloane, Transforms
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FORMULA
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Generalized Fibonacci sequence for (unsigned) Laguerre triangle A021009. a(n+1)=sum{k=0..floor(n/2), C(n-k, k)(n-k)!/k!}. - Paul Barry (pbarry(AT)wit.ie), May 10 2004
a(-n)=a(n). - Michael Somos Sep 25 2005
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PROGRAM
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(PARI) a(n)=contfracpnqn(vector(abs(n), i, i))[1, 2] /* Michael Somos Sep 25 2005 */
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CROSSREFS
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A column of A058294. Cf. A001053.
A127701 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 29 2008]
Sequence in context: A157313 A030971 A006932 this_sequence A162286 A032269 A041737
Adjacent sequences: A001037 A001038 A001039 this_sequence A001041 A001042 A001043
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KEYWORD
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easy,nonn,nice,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy
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