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A151884
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Let g be a permutation of [1..n] having say j_i cycles of length i, with Sum_i i*j_i = n; sequence gives Sum_g Sum_{i odd} (j_i)^2.
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4
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1, 4, 14, 56, 304, 1904, 14048, 112384, 1051776, 10662912, 120920832, 1451049984, 19342651392, 272576268288, 4175822315520, 66813157048320, 1156746459709440, 20900477925457920, 403511454289428480, 8070229085788569600, 171907712809736601600
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