OFFSET
0,2
COMMENTS
A partition of {-n,...,-1,1,...,n} into nonempty subsets X_1,...,X_r is called `symmetric' if for each i -X_i = X_j for some j. a(n) is the number of such symmetric partitions such that none of the X_i are of the form {j,-j}.
FORMULA
E.g.f. (for offset 1): -1 + exp(-x+sum(j=1,2,(exp(j*x)-1)/j)) [Joerg Arndt, Apr 29 2011]
EXAMPLE
a(2)=4 because the relevant partitions of {-2,-1,1,2} are {-2|-1|1|2}, {-2,-1|1,2}, {-2,1|-1,2} and {-2,-1,1,2}.
PROG
(PARI)
x = 'x + O('x^16);
egf = -1 + exp(-x+sum(j=1, 2, (exp(j*x)-1)/j))
/* egf == +x +2*x^2 +5/2*x^3 +25/8*x^4 +... (i.e., for offset 1) */
Vec( serlaplace(egf) )
/* Joerg Arndt, Apr 29 2011 */
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
James East, Sep 04 2003
EXTENSIONS
More terms from Joerg Arndt, Apr 29 2011.
Definition shortened by M. F. Hasler, Oct 21 2012
STATUS
approved