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In combinatorics, the Schröder–Hipparchus numbers form an integer sequence that can be used to count the number of plane trees with a given set of leaves, the number of ways of inserting parentheses into a sequence, and the number of ways of dissecting a convex polygon into smaller polygons by inserting diagonals. These numbers begin 1, 1, 3, 11, 45, 197, 903, 4279, 20793, 103049, ... (sequence in the OEIS).

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  • Schröder–Hipparchus number
  • Nombre de Schröder-Hipparque
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  • En thĂ©orie des nombres, les nombres de Schröder-Hipparque forment une suite d'entiers qui servent Ă  compter les arbres planaires avec un ensemble donnĂ© de feuilles, les insertions de parenthèses dans une suite, et le nombre de façons de dĂ©couper un polygone convexe en polygones plus petits par l'insertion de diagonales. Cette suite de nombres commence par 1, 1, 3, 11, 45, 197, 903, 4279, 20793, 103049, 518859,... (c'est la suite de l'OEIS).
  • In combinatorics, the Schröder–Hipparchus numbers form an integer sequence that can be used to count the number of plane trees with a given set of leaves, the number of ways of inserting parentheses into a sequence, and the number of ways of dissecting a convex polygon into smaller polygons by inserting diagonals. These numbers begin 1, 1, 3, 11, 45, 197, 903, 4279, 20793, 103049, ... (sequence in the OEIS).
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  • Susanne Bobzien
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  • Susanne
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  • Bobzien
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  • Super Catalan Number
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  • SuperCatalanNumber
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  • En thĂ©orie des nombres, les nombres de Schröder-Hipparque forment une suite d'entiers qui servent Ă  compter les arbres planaires avec un ensemble donnĂ© de feuilles, les insertions de parenthèses dans une suite, et le nombre de façons de dĂ©couper un polygone convexe en polygones plus petits par l'insertion de diagonales. Cette suite de nombres commence par 1, 1, 3, 11, 45, 197, 903, 4279, 20793, 103049, 518859,... (c'est la suite de l'OEIS). Ils sont aussi appelĂ©s nombres super-Catalans, petits nombres de Schröder, ou nombres d'Hipparque, d'après Eugène Charles Catalan et ses nombres de Catalan, Ernst Schröder et ses (grands) nombres de Schröder très voisins, et d'après le mathĂ©maticien et astronome grec Hipparque qui, selon Plutarque, connaissait certainement ces nombres.
  • In combinatorics, the Schröder–Hipparchus numbers form an integer sequence that can be used to count the number of plane trees with a given set of leaves, the number of ways of inserting parentheses into a sequence, and the number of ways of dissecting a convex polygon into smaller polygons by inserting diagonals. These numbers begin 1, 1, 3, 11, 45, 197, 903, 4279, 20793, 103049, ... (sequence in the OEIS). They are also called the super-Catalan numbers, the little Schröder numbers, or the Hipparchus numbers, after Eugène Charles Catalan and his Catalan numbers, Ernst Schröder and the closely related Schröder numbers, and the ancient Greek mathematician Hipparchus who appears from evidence in Plutarch to have known of these numbers.
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