%I A001517 M3062 N1240
%S A001517 1,3,19,193,2721,49171,1084483,28245729,848456353,28875761731,
%T A001517 1098127402131,46150226651233,2124008553358849,106246577894593683,
%U A001517 5739439214861417731,332993721039856822081,20651350143685984386753
%N A001517 Bessel polynomials y_n(x) (see A001498) evaluated at 2.
%C A001517 Numerators of successive convergents to e using continued fraction 1+2/
               (1+1/(6+1/(10+1/(14+1/(18+1/(22+1/26...)))))).
%C A001517 Number of ways to use the elements of {1,..,k}, n<=k<=2n, once each to 
               form a collection of n lists, each having length 1 or 2. - Bob Proctor, 
               Apr 18 2005, Jun 26 2006
%D A001517 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001517 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001517 L. Euler, 1737.
%D A001517 J. W. L. Glaisher, Reports of British Assoc. Adv. Sci., 1871, pp. 16-18.
%D A001517 I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products, 
               6th ed., Section 0.126, p. 2.
%D A001517 D. H. Lehmer, Review of various tables by P. Pederson, Math. Comp., 2 
               (1946), 68-69.
%D A001517 J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
%H A001517 T. D. Noe, <a href="b001517.txt">Table of n, a(n) for n=0..100</a>
%H A001517 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=131">
               Encyclopedia of Combinatorial Structures 131</a>
%H A001517 <a href="Sindx_Par.html#partN">Index entries for related partition-counting 
               sequences</a>
%H A001517 <a href="Sindx_Be.html#Bessel">Index entries for sequences related to 
               Bessel functions or polynomials</a>
%F A001517 a(n) = Sum_{k=0..n} (n+k)!/(k!*(n-k)!) = (e/pi)^(1/2) K_{n+1/2}(1/2).
%F A001517 a(n) = (4n-2)a(n-1) + a(n-2), n>=2.
%F A001517 a(n) = (1/n!)*Sum_{k=0..n} (-1)^(n+k)*binomial(n,k)*A000522(n+k). - Vladeta 
               Jovovic (vladeta(AT)eunet.rs), Sep 30 2006
%o A001517 (PARI) a(n)=sum(k=0,n,(n+k)!/k!/(n-k)!)
%Y A001517 Essentially the same as A080893.
%Y A001517 a(n) = A099022(n)/n!.
%Y A001517 Partial sums: A105747.
%Y A001517 Replace "lists" by "sets" in comment: A001515.
%Y A001517 Cf. A001515, A001518, A002119, A053556, A053557.
%Y A001517 Sequence in context: A119394 A101481 A155805 this_sequence A080893 A028854 
               A108292
%Y A001517 Adjacent sequences: A001514 A001515 A001516 this_sequence A001518 A001519 
               A001520
%K A001517 nonn,easy,nice
%O A001517 0,2
%A A001517 N. J. A. Sloane (njas(AT)research.att.com).
%E A001517 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 03 2000
%E A001517 Additional comments from Michael Somos, Jul 15, 2002.