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A101292 a(n) = n! + Sum_{i=1..n} i. 2
1, 2, 5, 12, 34, 135, 741, 5068, 40356, 362925, 3628855, 39916866, 479001678, 6227020891, 87178291305, 1307674368120, 20922789888136, 355687428096153, 6402373705728171, 121645100408832190, 2432902008176640210, 51090942171709440231, 1124000727777607680253 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Called "factoriangular" numbers by Castillo. - N. J. A. Sloane, Aug 30 2016
The only Fibonacci numbers in this sequence are 1, 2, 5, 34. [Ruiz and Luca, verifying a conjecture of Castillo] - Eric M. Schmidt, Nov 07 2017
LINKS
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.
FORMULA
a(n) = n! + n*(n+1)/2.
EXAMPLE
a(3) = 3! + (1 + 2 + 3) = 12.
a(5) = 5! + (1 + 2 + 3 + 4 + 5) = 135.
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
MATHEMATICA
Array[#! + # (# + 1)/2 &, 23, 0] (* Michael De Vlieger, Nov 12 2019 *)
CROSSREFS
Cf. A275928.
Sequence in context: A176638 A131467 A000103 * A350441 A181899 A131267
KEYWORD
base,nonn,easy
AUTHOR
Parthasarathy Nambi, Dec 21 2004
EXTENSIONS
More terms from Emeric Deutsch, Mar 12 2005
a(0)=1 prepended by Alois P. Heinz, Aug 30 2016
STATUS
approved

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Last modified February 21 10:54 EST 2024. Contains 370233 sequences. (Running on oeis4.)