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Preheat oven to 350°F with rack in middle. Butter a 9-inch round cake pan (2 inches deep). Line bottom with a round of parchment paper, then butter parchment.
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Sift together flour, baking powder, baking soda, and salt.
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Beat together butter and sugar in a large bowl with an electric mixer until pale and fluffy. Beat in vanilla. Add eggs 1 at a time, beating well after each addition. With mixer at low speed, beat in buttermilk until just combined. Add flour mixture in 3 batches, mixing after each addition until just combined.
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Spread batter in cake pan, smoothing top. Rap pan on counter several times to eliminate air bubbles.
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Bake until golden and a wooden pick inserted in center comes out clean, 35 to 40 minutes. Cool in pan on a rack 10 minutes. Run a knife around edge of cake to loosen, then invert onto a plate. Discard paper and reinvert cake onto rack to cool completely.