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