%I A001040 M2863 N1151
%S A001040 0,1,1,3,10,43,225,1393,9976,81201,740785,7489051,83120346,1004933203,
               13147251985,
%T A001040 185066460993,2789144166880,44811373131073,764582487395121,13807296146243251,
%U A001040 263103209266016890,5275871481466581051,111056404320064218961,2448516766522879398193
%N A001040 a(n+1) = n*a(n) + a(n-1).
%C A001040 If the initial 0 and 1 are omitted, CONTINUANT transform of 1, 2, 3, 
               4, 5, ...
%C A001040 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.
%C A001040 Starting (1, 3, 10, 43,...) = eigensequence of triangle A127701 [From 
               Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 29 2008]
%D A001040 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001040 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001040 Archimedeans Problems Drive, Eureka, 22 (1959), 15.
%H A001040 T. D. Noe, <a href="b001040.txt">Table of n, a(n) for n=0..100</a>
%H A001040 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%F A001040 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
%F A001040 a(-n)=a(n). - Michael Somos Sep 25 2005
%o A001040 (PARI) a(n)=contfracpnqn(vector(abs(n),i,i))[1,2] /* Michael Somos Sep 
               25 2005 */
%Y A001040 A column of A058294. Cf. A001053.
%Y A001040 A127701 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 29 2008]
%Y A001040 Sequence in context: A157313 A030971 A006932 this_sequence A162286 A032269 
               A041737
%Y A001040 Adjacent sequences: A001037 A001038 A001039 this_sequence A001041 A001042 
               A001043
%K A001040 easy,nonn,nice,frac
%O A001040 0,4
%A A001040 N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy