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%I #7 May 24 2018 16:04:30
%S 2,6,12,26,44,86,136,239,376,613,930,1485,2194,3355,4948,7372,10656,
%T 15660,22359,32308
%N Number of skew partitions whose quotient diagram is connected and whose numerator has weight n.
%C The diagram of a connected skew partition is required to be connected as a polyomino but can have empty rows or columns.
%e The a(3) = 12 skew partitions:
%e (3)/() (3)/(1) (3)/(2) (3)/(3)
%e (21)/() (21)/(11) (21)/(2) (21)/(21)
%e (111)/() (111)/(1) (111)/(11) (111)/(111)
%t undcon[y_]:=Select[Tuples[Range[0,#]&/@y],Function[v,GreaterEqual@@v&&With[{r=Select[Range[Length[y]],y[[#]]=!=v[[#]]&]},Or[Length[r]<=1,And@@Table[v[[i]]<y[[i+1]],{i,Range[Min@@r,Max@@r-1]}]]]]];
%t Table[Total[Length/@undcon/@IntegerPartitions[n]],{n,10}]
%Y Cf. A000085, A000898, A006958, A138178, A238690, A259479, A259480, A297388, A299925, A299926, A300118, A300122, A300123, A300124.
%K nonn,more
%O 1,1
%A _Gus Wiseman_, Feb 25 2018
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