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 A038507 n! + 1. (Formerly N0107) 55
 2, 2, 3, 7, 25, 121, 721, 5041, 40321, 362881, 3628801, 39916801, 479001601, 6227020801, 87178291201, 1307674368001, 20922789888001, 355687428096001, 6402373705728001, 121645100408832001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS "For n = 4, 5 and 7, n!+1 is a square. Sierpiński asked if there are any other values of n with this property." p. 82 of Ogilvy and Anderson (see A146968). Number of {12,12*,1*2,21*,2*1}-avoiding signed permutations in the hyperoctahedral group. REFERENCES C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, Oxford University Press, 1966, p. 82. Wacław Sierpiński, On some unsolved problems of arithmetics, Scripta Mathematica, vol. 25 (1960), p. 125. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..300 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 763 and Encyclopedia of Combinatorial Structures 834 [broken links] T. Mansour and J. West, Avoiding 2-letter signed patterns, arXiv:math/0207204 [math.CO], 2002. R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670, 2012 - From N. J. A. Sloane, Jun 13 2012 G. P. Michon, Wilson's Theorem Hisanori Mishima, Factorizations of many number sequences Hisanori Mishima, Factorizations of many number sequences Andrew Walker, Factors of n! +- 1 Arthur T. White, Ringing the changes, Math. Proc. Cambridge Philos. Soc. 94 (1983), no. 2, 203-215. R. G. Wilson v, Explicit factorizations FORMULA a(n) = n * (a(n-1) - 1) + 1. - Reinhard Zumkeller, Mar 20 2013 0 = a(n)*(a(n+1) - 5*a(n+2) + 5*a(n+3) - a(n+4)) + a(n+1)*(a(n+1) + a(n+2) - 6*a(n+3) + 2*a(n+4)) + a(n+2)*(3*a(n+2) - a(n+3) - a(n+4)) + a(n+3)*(a(n+3)) if n>=0. - Michael Somos, Apr 23 2014 EXAMPLE G.f. = 2 + 2*x + 3*x^2 + 7*x^3 + 25*x^4 + 121*x^5 + 721*x^6 + 5041*x^7 + ... MATHEMATICA Range[0, 20]!+1 (* Harvey P. Dale, May 06 2012 *) PROG (MAGMA) [Factorial(n) +1: n in [0..25]]; // Vincenzo Librandi, Jul 20 2011 (Maxima) A038507(n):= n!+1\$ makelist(A038507(n), n, 0, 30); /* Martin Ettl, Nov 03 2012 */ (PARI) a(n)=n!+1 \\ Charles R Greathouse IV, Nov 20 2012 (Haskell) a038507 = (+ 1) . a000142 a038507_list = 2 : f 1 2 where    f x y = z : f (x + 1) z where z = x * (y - 1) + 1 -- Reinhard Zumkeller, Mar 20 2013 CROSSREFS Cf. A000142, A002583, A002981, A033312, A051301, A056111. Sequence in context: A076996 A139148 A185387 * A077001 A180996 A087522 Adjacent sequences:  A038504 A038505 A038506 * A038508 A038509 A038510 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Additional comments from Jason Earls (zevi_35711(AT)yahoo.com), Apr 01 2001 Numericana.com URL fixed by Gerard P. Michon, Mar 30 2010 Entry revised by N. J. A. Sloane, Jun 10 2012 STATUS approved

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Last modified December 7 07:15 EST 2016. Contains 278841 sequences.