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Segner's Recurrence Formula

Segner's recurrence formula is the recurrence relation

E_n=E_2E_(n-1)+E_3E_(n-2)+...+E_(n-1)E_2

for integer n>=3, with E_2=1. It gives the solution E_n=C_(n-2) to Euler's polygon division problem for n>=2, where C_n is a Catalan number (Segner 1761).

See also

Catalan Number, Euler's Polygon Division Problem

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References

Segner, J. A. "Enumeratio modorum quibus figurae planae rectilineae per diagonales dividuntur in triangula." Novi Comment. Acad. Sci. Imp. Petropol. 7, 203-210, 1761. https://www.math.ucla.edu/~pak/lectures/Cat/Segner1.pdf.

Referenced on Wolfram|Alpha

Segner's Recurrence Formula

Cite this as:

Weisstein, Eric W. "Segner's Recurrence Formula." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SegnersRecurrenceFormula.html

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