0,2

Numerators of successive convergents to e using continued fraction 1+2/(1+1/(6+1/(10+1/(14+1/(18+1/(22+1/26...)))))).

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

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).

L. Euler, 1737.

J. W. L. Glaisher, Reports of British Assoc. Adv. Sci., 1871, pp. 16-18.

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products, 6th ed., Section 0.126, p. 2.

D. H. Lehmer, Review of various tables by P. Pederson, Math. Comp., 2 (1946), 68-69.

J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.

T. D. Noe, Table of n, a(n) for n=0..100

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 131

Index entries for related partition-counting sequences

Index entries for sequences related to Bessel functions or polynomials

a(n) = Sum_{k=0..n} (n+k)!/(k!*(n-k)!) = (e/pi)^(1/2) K_{n+1/2}(1/2).

a(n) = (4n-2)a(n-1) + a(n-2), n>=2.

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

(PARI) a(n)=sum(k=0, n, (n+k)!/k!/(n-k)!)

Essentially the same as A080893.

a(n) = A099022(n)/n!.

Partial sums: A105747.

Replace "lists" by "sets" in comment: A001515.

Cf. A001515, A001518, A002119, A053556, A053557.

Sequence in context: A119394 A101481 A155805 this_sequence A080893 A028854 A108292

Adjacent sequences: A001514 A001515 A001516 this_sequence A001518 A001519 A001520

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 03 2000

Additional comments from Michael Somos, Jul 15, 2002.