|
| |
|
|
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
|
|
|
|
1, 4, 15, 75, 428, 2781, 20093, 159340, 1372163, 12725447, 126238060, 1332071241, 14881206473, 175297058228, 2169832010759, 28136696433171, 381199970284620, 5383103100853189, 79065882217154085, 1205566492711167004, 19049651311462785947
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
