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A086365
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n-th Bell number of type D. 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}.
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1
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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; internal format)
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OFFSET
| 0,2
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FORMULA
| E.g.f. (with another 1 prepended): exp(-x+sum(j=1,2,(exp(j*x)-1)/j)) [Joerg Arndt, Apr 29 2011]
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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}.
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PROG
| (Pari) x='x+O('x^66); /* that many terms */
egf=exp(-x+sum(j=1, 2, (exp(j*x)-1)/j)) - 1; /* = +x +2*x^2 +5/2*x^3 +25/8*x^4 +... */
Vec(serlaplace(egf)) /* show terms */ /* Joerg Arndt, Apr 29 2011 */
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CROSSREFS
| Cf. A002872, A086364.
Sequence in context: A171005 A020082 A020037 * A032270 A198057 A002750
Adjacent sequences: A086362 A086363 A086364 * A086366 A086367 A086368
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KEYWORD
| easy,nonn
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AUTHOR
| James East (jameseastseq(AT)hotmail.com), Sep 04 2003
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EXTENSIONS
| More terms by Joerg Arndt, Apr 29 2011.
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