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A027295
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a(n) = Sum_{k=0..m-1} T(n,k) * T(n,k+1), where m=n for n=0,1 and m=floor((n+3)/2) for n >= 2, and T given by A026022.
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0
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1, 4, 15, 52, 195, 676, 2555, 8976, 34098, 121448, 463067, 1669340, 6384287, 23251620, 89157557, 327523680, 1258803182, 4658150520, 17940605163, 66803546472, 257777882894, 965023761064, 3730202020650, 14029655954272, 54315578806820, 205120107930192
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