A086365 n-th Bell number of type D: Number of symmetric partitions of {-n,...,n}\{0} such that none of the subsets is of the form {j,-j}.

1, 4, 15, 75, 428, 2781, 20093, 159340, 1372163, 12725447, 126238060, 1332071241, 14881206473, 175297058228, 2169832010759, 28136696433171, 381199970284620, 5383103100853189, 79065882217154085, 1205566492711167004, 19049651311462785947

Offset: 0

Author

James East, Sep 04 2003

Keywords

• easy
• nonn
• changed

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}.

Examples

			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}.
		

Crossrefs

Cf. A002872, A086364.

Programs

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 */

Formula

E.g.f. (for offset 1): -1 + exp(-x + Sum_{j=1..2} (exp(j*x)-1)/j). - Joerg Arndt, Apr 29 2011

Extensions

More terms from Joerg Arndt, Apr 29 2011

Definition shortened by M. F. Hasler, Oct 21 2012