|
| |
|
|
A011965
|
|
Second differences of Bell numbers.
|
|
7
| |
|
|
1, 2, 7, 27, 114, 523, 2589, 13744, 77821, 467767, 2972432, 19895813, 139824045, 1028804338, 7905124379, 63287544055, 526827208698, 4551453462543, 40740750631417, 377254241891064, 3608700264369193, 35613444194346451, 362161573323083920, 3790824599495473121
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| 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, 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
|
|
|
REFERENCES
| Olivier Gerard and Karol A. Penson, A budget of set partition statistics, in preparation, unpublished as of Sep 22 2011.
|
|
|
LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..250
|
|
|
FORMULA
| a(n) = A005493(n)-A005493(n-1).
E.g.f.: exp(exp(x)-1)*(exp(2*x)-exp(x)+1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 11 2003
a(n) = A000110(n) - 2*A000110(n-1) + A000110(n-2). - Andrey Goder (andy.goder(AT)gmail.com), Dec 17 2007
|
|
|
MAPLE
| a:= n-> add ((-1)^k *binomial(2, k) *combinat['bell'](n+k), k=0..2): seq (a(n), n=0..20); # Alois P. Heinz, Sep 05 2008
|
|
|
MATHEMATICA
| Differences[BellB[Range[0, 30]], 2] (* From Vladimir Joseph Stephan Orlovsky, May 25 2011 *)
|
|
|
CROSSREFS
| Cf. A000110, A005493.
Sequence in context: A127897 A180473 A154108 * A150629 A150630 A150631
Adjacent sequences: A011962 A011963 A011964 * A011966 A011967 A011968
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
