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  "body": "\n## Summary\n\nThe symbolic method translates a description of a combinatorial class into an equation for its [[generating function|0PHAC833JF]], see the [[definition|39HWNYW5EF]].\nEach construction, such as disjoint union, pair or sequence, has a fixed rule that acts on generating functions.\nUnlabelled classes lead to ordinary generating functions, and labelled classes lead to [[exponential generating functions|0JHXPVFKT0]].\nIt is the first part of [[analytic combinatorics|YJK71RKVEB]], whose second part extracts asymptotics from the equations.\n\n## Explanations\n\n### L1 human\n\nA binary tree is either empty, or a root with a left and a right binary tree.\nThe symbolic method turns this sentence directly into the equation $B(z) = 1 + z B(z)^2$.\nHere \"or\" becomes $+$, \"with\" becomes a product, and the root becomes a factor $z$.\nSolving the equation gives the [[Catalan numbers|0YWZJEABB2]] as the coefficients of $B(z)$.\nThe point is that one never counts by hand: the grammar of the objects does the work.\n",
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