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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

REFERENCES

R. 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.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..450

Romer C. Castillo, Generalized Factoriangular Numbers and Factoriangular Triangles, International Journal of Advanced Research and Publications, 2017.

R. 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.

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

CROSSREFS

Cf. A275928.

Sequence in context: A176638 A131467 A000103 * A181899 A131267 A266931

Adjacent sequences:  A101289 A101290 A101291 * A101293 A101294 A101295

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 November 14 06:49 EST 2018. Contains 317162 sequences. (Running on oeis4.)