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Search: id:A011965
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| A011965 |
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Second differences of Bell numbers. |
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+0
5
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| 1, 2, 7, 27, 114, 523, 2589, 13744, 77821, 467767, 2972432, 19895813, 139824045, 1028804338, 7905124379, 63287544055, 526827208698, 4551453462543, 40740750631417, 377254241891064, 3608700264369193
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Number of partitions of n+3 with at least one singleton and with the smallest element in a singleton equal to 3. Alternatively, number of partitions of n+3 with at least one singleton and with the largest element in a singleton equal to n+1. - Olivier GERARD (olivier.gerard(AT)gmail.com), Oct 29 2007
Out of the A005493(n) set partitions with a specific two elements clustered separately, number that have a different set of two elements clustered separately. - Andrey Goder (andy.goder(AT)gmail.com), Dec 17 2007
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REFERENCES
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Olivier Gerard and Karol A. Penson, A budget of set partition statistics, in preparation.
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FORMULA
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E.g.f.: exp(exp(x)-1)*(exp(2*x)-exp(x)+1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 11 2003
a(n) = Bell(n) - 2 Bell(n-1) + Bell(n - 2) - Andrey Goder (andy.goder(AT)gmail.com), Dec 17 2007
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MAPLE
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a:= n-> sum ((-1)^k *binomial(2, k) *combinat['bell'](n+k), k=0..2): seq (a(n), n=0..20); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 05 2008]
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CROSSREFS
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Cf. A000110.
Cf. A005493.
Adjacent sequences: A011962 A011963 A011964 this_sequence A011966 A011967 A011968
Sequence in context: A106225 A127897 A154108 this_sequence A150629 A150630 A150631
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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