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MATHEMATICA
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sb[ n_, k_ ] := sb[ n, k ]=b[ n+1-k, 1 ]+If[ n<2k, 0, sb[ n-k, k ] ]; b[ 1, 1 ] := 1;
b[ n_, 1 ] := b[ n, 1 ]=Sum[ b[ i, 1 ]sb[ n-1, i ]i, {i, 1, n-1} ]/(n-1);
b[ n_, k_ ] := b[ n, k ]=Sum[ b[ i, 1 ]b[ n-i, k-1 ], {i, 1, n-1} ];
Table[ b[ i, 3 ]/2+5b[ i, 4 ]/8+Sum[ b[ i, j ], {j, 5, i} ]+If[ OddQ[ i ], 0, 7b[ i/2, 2 ]/8
+If[ OddQ[ i/2 ], 0, b[ i/4, 1 ]/4 ]+Sum[ b[ i/2, j ], {j, 3, i/2} ] ]
+Sum[ b[ j, 1 ](b[ i-2j, 1 ]/2+b[ i-2j, 2 ]/4)+Sum[ If[ OddQ[ k ], b[ j,
(k-1)/2 ]b[ i-2j, 1 ], 0 ], {k, 5, i} ], {j, 1, (i-1)/2} ], {i, 3, 30} ]
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