0,3

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

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).

Leo Chao, Paul DesJarlais and John L Leonard, A binomial identity, via derangements, Math. Gaz. 89 (2005), 268-270..

L. Euler, 1737.

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

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

Index entries for sequences related to Bessel functions or polynomials

a(n) = -2(2n-1)*a(n-1) + a(n-2). - T. D. Noe, Oct 26 2006

If y = x + Sum_{k>1} A005363(k)*x^k/k!, then y = x + Sum{k>1} a(k-2)(-y)^k/k!. - Michael Somos Apr 02 2007

a(-n-1)= a(n). - Michael Somos Apr 02 2007

(PARI) {a(n)= if(n<0, n=-n-1); sum(k=0, n, (2*n-k)!/ (k!*(n-k)!)* (-1)^(n-k) )} /* Michael Somos Apr 02 2007 */

(PARI) {a(n)= local(A); if(n<0, n= -n-1); A= sqrt(1 +4*x +x*O(x^n)); n!*polcoeff( exp((A-1)/2)/A, n)} /* Michael Somos Apr 02 2007 */

(PARI) {a(n)= local(A); if(n<0, n= -n-1); n+=2 ; for(k= 1, n, A+= x*O(x^k); A= truncate( (1+x)* exp(A) -1-A) ); A+= x*O(x^n); A-= A^2; -(-1)^n*n!* polcoeff( serreverse(A), n)} /* Michael Somos Apr 02 2007 */

Cf. A001517, A053556, A053557, A001514, A065920, A065921, A065922, A065707, A000806, A006199, A065923.

See also A033815.

Polynomial coefficients are in A001498.

Sequence in context: A048552 A067307 A052390 this_sequence A146752 A022518 A113053

Adjacent sequences: A002116 A002117 A002118 this_sequence A002120 A002121 A002122

sign,easy,nice

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

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