0,4

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 A075744 A109186

Adjacent sequences: A000803 A000804 A000805 this_sequence A000807 A000808 A000809

sign,easy,nice

njas