A020549 a(n) = (n!)^2 + 1.
2, 2, 5, 37, 577, 14401, 518401, 25401601, 1625702401, 131681894401, 13168189440001, 1593350922240001, 229442532802560001, 38775788043632640001, 7600054456551997440001, 1710012252724199424000001, 437763136697395052544000001
Offset: 0
Keywords
References
- T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 147.
- F. Iacobescu, Smarandache Partition Type and Other Sequences, Bull. Pure Appl. Sciences, Vol. 16E, No. 2 (1997), pp. 237-240.
- H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 170-183.
- M. Le, On the Interesting Smarandache Product Sequences, Smarandache Notions Journal, Vol. 9, No. 1-2, 1998, 133-134.
- M. Le, The Primes in Smarandache Power Product Sequences, Smarandache Notions Journal, Vol. 9, No. 1-2, 1998, 96-97.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..250
- M. Fleuren, Smarandache Square Products.
- F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.
- Apoloniusz Tyszka, On sets X, subset of N, whose finiteness implies that we know an algorithm which for every n, element of N, decides the inequality max (X) < n, (2019).
- Apoloniusz Tyszka, On ZFC-formulae phi(x) for which we know a non-negative integer n such that max({x, element of N, phi(x)}) <= n if the set {x, element of N, phi(x)} is finite, 2019.
- Eric Weisstein's World of Mathematics, Factorial
- Eric Weisstein's World of Mathematics, Smarandache Sequences
Programs
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Maple
with(combinat):seq(fibonacci(3,n!), n=0..16); # Zerinvary Lajos, Apr 21 2008 [seq(n!^2+1,n=0..20)]; # N. J. A. Sloane, Feb 26 2017
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Mathematica
Table[(n!)^2 + 1, {n, 0, 20}] (* Vladimir Joseph Stephan Orlovsky, Apr 08 2011 *) -
PARI
a(n)=n!^2 + 1 \\ Charles R Greathouse IV, Nov 30 2016
Comments