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%I #10 May 24 2018 16:06:15
%S 1,0,1,1,0,0,1,0,2,1,0,1,1,0,0,1,0,0,1,0,3,1,0,0,3,0,3,2,1,0,0,0,0,1,
%T 0,3,1,0,4,2,0,0,1,0,0,1,0,1,6,0,0,3,1,0,4,0,5,0,0,0,1,1,8,1,0,0,0,0,
%U 0,2,1,0,0,0,6,4,0,0,1,0,6,1,0,6,5,0,6,3,1,2,10,0,0,1,0,0,0,0,0,8,1,0,0,0,0,0
%N Number of normal standard domino tableaux whose shape is the integer partition with Heinz number n.
%C 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. A standard domino tableau is a generalized Young tableau in which all rows and columns are weakly increasing and all regions are dominos. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e The a(75) = 6 tableaux:
%e 1 2 4 1 2 3 1 2 2 1 1 4 1 1 4 1 1 3
%e 1 2 4 1 2 3 1 3 3 2 3 4 2 2 4 2 2 3
%e 3 3 4 4 4 4 2 3 3 3 4 4
%Y Cf. A000085, A000712, A000898, A001222, A004003, A056239, A099390, A112798, A122111, A138178, A153452, A238690, A296150, A296188, A297388, A299926, A300060, A300061.
%K nonn
%O 1,9
%A _Gus Wiseman_, Feb 23 2018