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A152296
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Let f(M,N)=2^(-M)*sum_{i=0..N} {(-1)^{i}M!N!(2M-2i)!}/{i!(M-i)!(N-i)!6^{N-i}}; then a(n) = f(3n,n).
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2
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1, 6, 113400, 32901422400, 67651716132000000, 608762379843757339200000, 17903325789347617610786995200000, 1415199921956087613201896962521600000000, 261375521452474271183649591888039276441600000000, 101519644940256627137917269623207295713536128000000000000, 76392226231236455854222646891536244623780022885776896000000000000
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