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  "body": "\n## Description\n\nPascal's triangle is the triangular array of the [[binomial coefficients|092GEF38YD]].\nIts rows are numbered $n = 0, 1, 2, \\dots$ from the top.\nRow $n$ has $n + 1$ entries, $\\binom{n}{0}, \\binom{n}{1}, \\dots, \\binom{n}{n}$, from left to right.\n\nThe first five rows are these.\n$$\\begin{array}{ccccccccc} \u0026 \u0026 \u0026 \u0026 1 \u0026 \u0026 \u0026 \u0026 \\\\ \u0026 \u0026 \u0026 1 \u0026 \u0026 1 \u0026 \u0026 \u0026 \\\\ \u0026 \u0026 1 \u0026 \u0026 2 \u0026 \u0026 1 \u0026 \u0026 \\\\ \u0026 1 \u0026 \u0026 3 \u0026 \u0026 3 \u0026 \u0026 1 \u0026 \\\\ 1 \u0026 \u0026 4 \u0026 \u0026 6 \u0026 \u0026 4 \u0026 \u0026 1 \\end{array}$$\n\nEach row starts and ends with $1$.\nEach other entry is the sum of the two entries next to it in the row above, by [[Pascal's rule|0YRG241HQQ]].\n\n## Remarks\n\nRow $n$ lists the coefficients of $(x + y)^n$, by the [[binomial theorem|0EHWPWGHB2]].\nThe sum of row $n$ is $2^n$. This is the [[sum of binomial coefficients|0KAMF19NV8]].\nEach row is symmetric, by the [[symmetry of binomial coefficients|0R7JS3DP3W]].\n\n## Explanations\n\n### L1 human\n\nStart with a $1$ at the top. Each new row starts and ends with $1$, and each inside number is the sum of the two numbers above it.\nRow 4 is $1, 4, 6, 4, 1$, and these are the coefficients of $(x + y)^4$.\n",
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