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 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 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

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Last modified March 31 21:49 EDT 2020. Contains 333151 sequences. (Running on oeis4.)