Search: id:A035098
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%I A035098
%S A035098 1,2,4,11,36,135,566,2610,13082,70631,407846,2504071,16268302,111378678,
%T A035098 800751152,6027000007,47363985248,387710909055,3298841940510,
%U A035098 29119488623294,266213358298590,2516654856419723,24566795704844210
%N A035098 Near-Bell numbers: partitions of an n-multiset with multiplicities 1, 
               1, 1, ..., 1, 2.
%C A035098 A035098 and A000070 are near the two ends of a spectrum. Another way 
               to look at A000070 is as the number of partitions of an n-multiset 
               with multiplicities n-1, 1.
%C A035098 The very ends are the number of partitions and the Stirling numbers of 
               the second kind, which count the n-multiset partitions with multiplicities 
               n and 1,1,1,...,1, respectively.
%C A035098 Intermediate sequences are the number of ways of partitioning an n-multiset 
               with multiplicities some partition of n.
%F A035098 Sum_{k=0..n} Stirling2(n, k)*((k+1)*(k+2)/2+1). E.g.f.: 1/2*(1+exp(x))^2*exp(exp(x)-1). 
               (1/2)*(Bell(n)+Bell(n+1)+Bell(n+2)). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Sep 23 2003
%e A035098 a(3)=4 because there are 4 ways to partition the multiset {1,2,2} (with 
               multiplicities {1,2}): {{1,2,2}} {{1,2},{2}} {{1},{2,2}} {{1},{2},
               {2}}.
%p A035098 with (combinat):a:=n->floor(1/2*(bell(n)+bell(n+1)+bell(n+2))): seq(a(n), 
               n=-1..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 07 
               2007
%t A035098 The author has a Mathematica program to calculate these.
%Y A035098 Cf. A000070.
%Y A035098 Cf. A000110, A059606.
%Y A035098 Sequence in context: A071794 A107378 A086611 this_sequence A138301 A118182 
               A107107
%Y A035098 Adjacent sequences: A035095 A035096 A035097 this_sequence A035099 A035100 
               A035101
%K A035098 nonn
%O A035098 1,2
%A A035098 George Beck (beck(AT)wri.com)
%E A035098 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 23 2003

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