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