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A005095
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a(n) = n! + n.
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11
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1, 2, 4, 9, 28, 125, 726, 5047, 40328, 362889, 3628810, 39916811, 479001612, 6227020813, 87178291214, 1307674368015, 20922789888016, 355687428096017, 6402373705728018, 121645100408832019, 2432902008176640020, 51090942171709440021
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OFFSET
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0,2
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COMMENTS
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Every infinite, increasing, integer arithmetic progression meets this sequence infinitely often. - John Abbott (abbott(AT)dima.unige.it), Mar 06 2003
Largest k such that (k!-n!)/(k-n) is an integer. - Derek Orr, Apr 02 2014
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LINKS
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Aria Chen, Tyler Cummins, Rishi De Francesco, Jate Greene, Tanya Khovanova, Alexander Meng, Tanish Parida, Anirudh Pulugurtha, Anand Swaroop, and Samuel Tsui, Card Tricks and Information, arXiv:2405.21007 [math.HO], 2024. See p. 5.
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FORMULA
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E.g.f.: x*exp(x) + 1/(1-x). - Len Smiley, Dec 05 2001
(n-1)*(n-3)*a(n) -n*(n^2-3*n+1)*a(n-1) +n*(n-1)*(n-2)*a(n-2)=0. - R. J. Mathar, Oct 30 2015
a(n) +(-n-3)*a(n-1) +3*(n)*a(n-2) +(-3*n+5)*a(n-3) +(n-3)*a(n-4)=0. - R. J. Mathar, Oct 30 2015
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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