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The gamma function, which has the property to interpolate the factorial whenever the argument is an integer, is a special case (the caseg = 2) of the general term of the sequence factorial ofg-gonal numbers. In relation to this special case, a formula for calculating the general term of the sequence factorial of anyg-gonal number was obtained after considering some specific cases. Important properties on functional equations ofg-gonal sequence factorials are derived. [ABSTRACT FROM PUBLISHER]

In this note, we present an interesting approach to sum subseries in closed form. This approach seems to be not widely known and remains under-appreciated. Our study will lead to the discovery of results some of which have been known for a long time, some which were found only recently, as well as those which appear to be new. [ABSTRACT FROM AUTHOR]

This note generalizes the formula for the triangular number of the sum and product of two natural numbers to similar results for the triangular number of the sum and product of r natural numbers. The formula is applied to derive formula for the sum of an odd and an even number of consecutive triangular numbers. [ABSTRACT FROM AUTHOR]

Identifies figurate and pseudo-figurate numbers. Algebraic equations of the figurate and pseudo-figurate numbers; Derivation of pseudo-figurate numbers for certain polygons.

Focuses on the generation of square-triangular numbers. Definition; Formulae.

Examines properties of triangular numbers. Connection to Pascal numbers; Generalization of definition of triangular numbers; Relationships and patterns.

Presents a divisibility property of square triangular numbers (STN). A multiple of the integer 36 as the difference of any two alternate STN; Proof of the theorem.

Presents a generalization of Euler's reproductive properties of triangular numbers. Method for constructing numbers of higher indices.