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

0,2

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}.

Links

Table of n, a(n) for n=0..20.

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

Cf. A002872, A086364.

Sequence in context: A230741 A020082 A020037 * A032270 A198057 A263004

Adjacent sequences: A086362 A086363 A086364 * A086366 A086367 A086368

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