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A111752
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Number of partitions of {1,..,n} into lists with an even number of lists of size 1, where a list means an ordered subset (cf. A000262).
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6
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0, 3, 6, 49, 300, 2491, 22890, 239457, 2782584, 35595091, 496577070, 7499663953, 121855323876, 2118793593099, 39245026343250, 771255810671041, 16025261292247920, 350956070419872547, 8078570913162379734
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) + A111753(n) = A000262(n). [From David Wasserman (dwasserm(AT)earthlink.net), Feb 11 2009]
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FORMULA
| E.g.f.: cosh(x)*exp(x^2/(1-x)). More generally, e.g.f. for number of partitions of {1, 2, ...n} into lists with an even number of lists of size k is cosh(x^k)*exp(x/(1-x)-x^k).
E.g.f.: cosh(x)*exp(x^2/(1-x))=1/2*Q(0); Q(k)=1+((2x-1)^k)/( 1-x/(x+((2x-1)^k)*(k+1)*(1-x)/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Nov 17 2011
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CROSSREFS
| Cf. A000262, A113235, A063083, A062282, A111723, A111724, A111753.
Sequence in context: A197884 A032322 A203765 * A102931 A056447 A056437
Adjacent sequences: A111749 A111750 A111751 * A111753 A111754 A111755
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 19 2005; corrected Jun 06 2006
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EXTENSIONS
| More terms from David Wasserman (dwasserm(AT)earthlink.net), Feb 11 2009
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