A101292 a(n) = n! + Sum_{i=1..n} i.
1, 2, 5, 12, 34, 135, 741, 5068, 40356, 362925, 3628855, 39916866, 479001678, 6227020891, 87178291305, 1307674368120, 20922789888136, 355687428096153, 6402373705728171, 121645100408832190, 2432902008176640210, 51090942171709440231, 1124000727777607680253
Offset: 0
Examples
a(3) = 3! + (1 + 2 + 3) = 12. a(5) = 5! + (1 + 2 + 3 + 4 + 5) = 135.
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..450
- Eric F. Bravo, Carlos A. Gómez, and Florian Luca, Product of Consecutive Tribonacci Numbers With Only One Distinct Digit, J. Int. Seq., Vol. 22 (2019), Article 19.6.3.
- Romer C. Castillo, On the Sum of Corresponding Factorials and Triangular Numbers: Some Preliminary Results, Asia Pacific Journal of Multidisciplinary Research, Vol. 3, No. 4, November 2015 Part I.
- Romer C. Castillo, On the Sum of Corresponding Factorials and Triangular Numbers: Runsums, Trapezoids and Politeness, Asia Pacific Journal of Multidisciplinary Research, 3 (2015), 95-101.
- Romer C. Castillo, Generalized Factoriangular Numbers and Factoriangular Triangles, International Journal of Advanced Research and Publications, 2017.
- Romer C. Castillo, On the Generalization of Factoriangular Numbers, Asian Res. J. Math. (2022) Vol. 18, No. 5, 1-21, Art. No. ARJOM.86060.
- Carlos Alexis Gómez Ruiz and Florian Luca, Fibonacci factoriangular numbers, Indagationes Mathematicae, Volume 28, Issue 4, August 2017, p. 796-804.
Crossrefs
Cf. A275928.
Programs
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Maple
seq(n!+n*(n+1)/2,n=0..22); # Emeric Deutsch, Mar 12 2005 a:= proc(n) option remember; `if`(n<3, [1,2,5][n+1], ((11*n^2+10*n-70)*a(n-1)-(34*n^2-81*n+60)*a(n-2) +(23*n-10)*(n-2)*a(n-3))/(11*n-24)) end: seq(a(n), n=0..25); # Alois P. Heinz, Aug 30 2016
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Mathematica
Array[#! + # (# + 1)/2 &, 23, 0] (* Michael De Vlieger, Nov 12 2019 *)
Formula
a(n) = n! + n*(n+1)/2.
Extensions
More terms from Emeric Deutsch, Mar 12 2005
a(0)=1 prepended by Alois P. Heinz, Aug 30 2016
Comments