cp's OEIS Frontend

A299967 Number of normal generalized Young tableaux of size n with all rows and columns weakly increasing and all regions non-singleton skew-partitions.

%I A299967 #7 Feb 23 2018 18:53:38
%S A299967 1,0,2,3,13,32,121,376,1406,5030,19632,76334,314582,1308550,5667494,
%T A299967 24940458,113239394,523149560,2480434938,11968944532,59051754824
%N A299967 Number of normal generalized Young tableaux of size n with all rows and columns weakly increasing and all regions non-singleton skew-partitions.
%C A299967 A generalized Young tableau of shape y is an array obtained by replacing the dots in the Ferrers diagram of y with positive integers. A tableau is normal if its entries span an initial interval of positive integers.
%e A299967 The a(4) = 13 tableaux:
%e A299967 1 1 2 2   1 1 1 1
%e A299967 .
%e A299967 1 2 2   1 1 2   1 1 1
%e A299967 1       2       1
%e A299967 .
%e A299967 1 2   1 1   1 1
%e A299967 1 2   2 2   1 1
%e A299967 .
%e A299967 1 2  1 1   1 1
%e A299967 1    2     1
%e A299967 2    2     1
%e A299967 .
%e A299967 1   1
%e A299967 1   1
%e A299967 2   1
%e A299967 2   1
%t A299967 undptns[y_]:=DeleteCases[Select[Tuples[Range[0,#]&/@y],OrderedQ[#,GreaterEqual]&],0,{2}];
%t A299967 ehn[y_]:=ehn[y]=If[Total[y]=!=1,1,0]+Sum[ehn[c],{c,Select[undptns[y],Total[#]>1&&Total[y]-Total[#]>1&]}];
%t A299967 Table[Sum[ehn[y],{y,IntegerPartitions[n]}],{n,15}]
%Y A299967 Cf. A000085, A063834, A138178, A153452, A238690, A296188, A297388, A299925, A299926, A299966.
%K A299967 nonn,more
%O A299967 0,3
%A A299967 _Gus Wiseman_, Feb 22 2018