%I A011965
%S A011965 1,2,7,27,114,523,2589,13744,77821,467767,2972432,19895813,
%T A011965 139824045,1028804338,7905124379,63287544055,526827208698,
%U A011965 4551453462543,40740750631417,377254241891064,3608700264369193
%N A011965 Second differences of Bell numbers.
%C A011965 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
%C A011965 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
%D A011965 Olivier Gerard and Karol A. Penson, A budget of set partition statistics, 
               in preparation.
%F A011965 E.g.f.: exp(exp(x)-1)*(exp(2*x)-exp(x)+1). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Feb 11 2003
%F A011965 a(n) = Bell(n) - 2 Bell(n-1) + Bell(n - 2) - Andrey Goder (andy.goder(AT)gmail.com), 
               Dec 17 2007
%p A011965 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]
%Y A011965 Cf. A000110.
%Y A011965 Cf. A005493.
%Y A011965 Sequence in context: A106225 A127897 A154108 this_sequence A150629 A150630 
               A150631
%Y A011965 Adjacent sequences: A011962 A011963 A011964 this_sequence A011966 A011967 
               A011968
%K A011965 nonn,easy
%O A011965 0,2
%A A011965 N. J. A. Sloane (njas(AT)research.att.com).