Factoriangular number
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A factoriangular number is a natural number that is the sum of a triangular number and its corresponding factorial number.[1][2] The sequence of factoriangular numbers (sequence A101292 in the OEIS), starting at the 0th factoriangular number, is:[3][4]
- 1, 2, 5, 12, 34, 135, 741, 5068, 40356, 362925, 3628855, 39916866, 479001678, 6227020891, 87178291305, 1307674368120, 20922789888136, 355687428096153, 6402373705728171, 121645100408832190, 2432902008176640210, 51090942171709440231, 1124000727777607680253 ...
The factoriangular numbers are given by the following formula:[5][6]
References[edit]
- ↑ Castillo, Romer C. (November 2015). "On the Sum of Corresponding Factorials and Triangular Numbers: Some Preliminary Results" (PDF). Asia Pacific Journal of Multidisciplinary Research. 3 (4): 5–11. ISSN 2350-7756. Retrieved 22 January 2017.
- ↑ Castillo, Romer C. (November 2015). "On the Sum of Corresponding Factorials and Triangular Numbers: Runsums, Trapezoids and Politeness" (PDF). Asia Pacific Journal of Multidisciplinary Research. 3 (4): 95–101. ISSN 2350-7756. Retrieved 22 January 2017.
- ↑ Castillo, Romer C. (November 2015). "Sums of Two Triangulars and of Two Squares Associated with Sum of Corresponding Factorial and Triangular Number" (PDF). Asia Pacific Journal of Multidisciplinary Research. 3 (4): 28–36. ISSN 2350-7756. Retrieved 22 January 2017.
- ↑ Castillo, Romer C. (November 2015). "Recurrence Relations and Generating Functions of the Sequence of Sums of Corresponding Factorials and Triangular Numbers" (PDF). Asia Pacific Journal of Multidisciplinary Research. 3 (4): 165–169. ISSN 2350-7756. Retrieved 22 January 2017.
- ↑ "A101292 - OEIS". oeis.org. Retrieved 22 January 2017.
- ↑ Castillo, Romer C. (11 November 2016). "A Survey on Triangular Number, Factorial and Some Associated Numbers". Indian Journal of Science and Technology. 9 (41). doi:10.17485/ijst/2016/v9i41/85182. Retrieved 22 January 2017.
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