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We already showed that Betti numbers are all zero when w is not equal to hfor (w,h)-doubly weighted homology groups of some special pre Lie superalgebraand showed the first Betti number is 0 when w = h. In this note, we show thatthe second Betti number is 0 when w = h.

The second Betti number of doubly weighted homology groups of some pre Lie superalgebra