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- Pentatope_number abstract "A pentatope number is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row 1 4 6 4 1 either from left to right or from right to left. The first few numbers of this kind are : 1, 5, 15, 35, 70, 126, 210, 330, 495, 715, 1001, 1365 (sequence A000332 in OEIS)Pentatope numbers belong in the class of figurate numbers, which can be represented as regular, discrete geometric patterns. The formula for the nth pentatopic number is: Two of every three pentatope numbers are also pentagonal numbers. To be precise, the (3k − 2)th pentatope number is always the ((3k2 − k)/2)th pentagonal number and the (3k − 1)th pentatope number is always the ((3k2 + k)/2)th pentagonal number. The 3kth pentatope number is the generalized pentagonal number obtained by taking the negative index −(3k2 + k)/2 in the formula for pentagonal numbers. (These expressions always give integers).The infinite sum of the reciprocals of all pentatopal numbers is . This can be derived using telescoping series. Pentatopal numbers can also be represented as the sum of the first n tetrahedral numbers.".
- Pentatope_number thumbnail Pentatope_of_70_spheres_animation.gif?width=300.
- Pentatope_number wikiPageID "927274".
- Pentatope_number wikiPageRevisionID "599690515".
- Pentatope_number hasPhotoCollection Pentatope_number.
- Pentatope_number subject Category:Figurate_numbers.
- Pentatope_number type Abstraction100002137.
- Pentatope_number type Amount105107765.
- Pentatope_number type Attribute100024264.
- Pentatope_number type FigurateNumbers.
- Pentatope_number type Magnitude105090441.
- Pentatope_number type Number105121418.
- Pentatope_number type Property104916342.
- Pentatope_number comment "A pentatope number is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row 1 4 6 4 1 either from left to right or from right to left. The first few numbers of this kind are : 1, 5, 15, 35, 70, 126, 210, 330, 495, 715, 1001, 1365 (sequence A000332 in OEIS)Pentatope numbers belong in the class of figurate numbers, which can be represented as regular, discrete geometric patterns.".
- Pentatope_number label "Nombre pentatopique".
- Pentatope_number label "Numero pentatopico".
- Pentatope_number label "Pentatope number".
- Pentatope_number label "Pentatopzahl".
- Pentatope_number label "五胞体数".
- Pentatope_number label "五胞體數".
- Pentatope_number sameAs Pentatopzahl.
- Pentatope_number sameAs Zenbaki_pentatopiko.
- Pentatope_number sameAs Nombre_pentatopique.
- Pentatope_number sameAs Numero_pentatopico.
- Pentatope_number sameAs 五胞体数.
- Pentatope_number sameAs m.03qq3_.
- Pentatope_number sameAs Q1403502.
- Pentatope_number sameAs Q1403502.
- Pentatope_number sameAs Pentatope_number.
- Pentatope_number wasDerivedFrom Pentatope_number?oldid=599690515.
- Pentatope_number depiction Pentatope_of_70_spheres_animation.gif.
- Pentatope_number isPrimaryTopicOf Pentatope_number.
