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A101292
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a(n) = n! + Sum_{i=1..n} i.
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2
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1, 2, 5, 12, 34, 135, 741, 5068, 40356, 362925, 3628855, 39916866, 479001678, 6227020891, 87178291305, 1307674368120, 20922789888136, 355687428096153, 6402373705728171, 121645100408832190, 2432902008176640210, 51090942171709440231, 1124000727777607680253
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OFFSET
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0,2
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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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.
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FORMULA
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a(n) = n! + n*(n+1)/2.
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EXAMPLE
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a(3) = 3! + (1 + 2 + 3) = 12.
a(5) = 5! + (1 + 2 + 3 + 4 + 5) = 135.
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MAPLE
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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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CROSSREFS
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Cf. A275928.
Sequence in context: A176638 A131467 A000103 * A181899 A131267 A266931
Adjacent sequences: A101289 A101290 A101291 * A101293 A101294 A101295
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KEYWORD
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base,nonn,easy
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AUTHOR
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Parthasarathy Nambi, Dec 21 2004
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EXTENSIONS
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More terms from Emeric Deutsch, Mar 12 2005
a(0)=1 prepended by Alois P. Heinz, Aug 30 2016
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STATUS
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approved
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