0,4

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).

G. Kreweras and Y. Poupard, Sur les partitions en paires d'un ensemble fini totalement ordonne, Publications de l'Institut de Statistique de l'Universit\'{e} de Paris, 23 (1978), 57-74.

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

J. Touchard, Nombres exponentiels et nombres de Bernoulli, Canad. J. Math., 8 (1956), 305-320.

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

Index entries for sequences related to Bessel functions or polynomials

E.g.f.: exp(sqrt(1+2*x)-1)/sqrt(1+2*x). - Michael Somos, Feb 16, 2002

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

If y = x + Sum_{k>1} A000272(k)*x^k/k!, then y = x + Sum{k>1} a(k-2)(-y)^k/k!. - Michael Somos Sep 07 2005

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

a(n)=sum(A001498(n,m)*(-1)^m,m=0..n), n>=0 (alternating row sums of Bessel triangle).

A000806 := proc(n) option remember; if n<=1 then n else (2*n+1)*A000806(n-1)+A000806(n-2); fi; end; # for unsigned version

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

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

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

Cf. A001515.

Polynomial coefficients are in A001498. Cf. A003436.

Cf. A101682.

Sequence in context: A091161 A135149 A067305 this_sequence A127132 A141764 A075744

Adjacent sequences: A000803 A000804 A000805 this_sequence A000807 A000808 A000809

sign,easy,nice

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