This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A006967 M3229 #91 Feb 16 2025 08:32:31 %S A006967 1,1,2,4,4,8,24,32,40,120,296,648,1328,3200,9912,25592,55920,143192, %T A006967 510696,1451296,3497344,10451824,38570704,118914992,315235872, %U A006967 1014824752,3963684496,13166130152,37846301904,130507967088,533318630936,1884550215976,5800121391936 %N A006967 Number of graceful permutations of length n. %C A006967 Also the number of graceful labelings of the path graph P_n. - _Eric W. Weisstein_, Mar 31 2020 %D A006967 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %D A006967 H. S. Wilf and N. Yoshimura, Ranking rooted trees and a graceful application, in Discrete Algorithms and Complexity (Proceedings of the Japan-US joint seminar, 1986, Kyoto, Japan), edited by D. Johnson, T. Nishizeki, A. Nozaki and H. S. Wilf, Academic Press, NY, 1987, pp. 341-350. %H A006967 Michal Adamaszek, Don Knuth, <a href="/A006967/b006967.txt">Table of n, a(n) for n = 0..41</a>, a(41) from Don Knuth. %H A006967 M. Adamaszek, <a href="https://arxiv.org/abs/math/0608513">Efficient enumeration of graceful permutations</a>, arXiv:math/0608513 [math.CO], 2006. %H A006967 Gheorghe Coserea, <a href="/A006967/a006967.txt">Solutions for n=5</a>. %H A006967 Gheorghe Coserea, <a href="/A006967/a006967_1.txt">Solutions for n=6</a>. %H A006967 Gheorghe Coserea, <a href="/A006967/a006967.mzn.txt">MiniZinc model for generating solutions</a>. %H A006967 Don Knuth, <a href="http://cs.stanford.edu/~knuth/programs/back-graceful-perms.w">This program finds all of the nonisomorphic graceful labelings of the path P_n</a> %H A006967 Don Knuth, <a href="http://cs.stanford.edu/~knuth/programs/zddl-graceful-perms.w">This program outputs ZDDL for all of the nonisomorphic graceful labelings of the path P_n</a> %H A006967 Md Masbaul Alam Polash, M. A. Hakim Newton, Abdul Sattar, <a href="https://doi.org/10.1007/s10601-016-9261-y">Constraint-directed search for all-interval series</a>, Constraints, July 2017, Volume 22, Issue 3, pp 403-431. See page 426. %H A006967 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GracefulLabeling.html">Graceful Labeling</a> %H A006967 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GracefulPermutation.html">Graceful Permutation</a> %H A006967 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PathGraph.html">Path Graph</a> %H A006967 J. Wodlinger, <a href="http://summit.sfu.ca/item/12222">Costas arrays, Golomb rulers and wavelength isolation sequence pairs, M.S. Dissertation</a>, Math. Dept., Simon Fraser University, Spring 2012; - From _N. J. A. Sloane_, Oct 15 2012 %F A006967 a(n) = n! - A084894(n). - _Jon Perry_, Jun 10 2003 %o A006967 (CWEB) @ See Knuth link. %Y A006967 Cf. A084894. %K A006967 nonn,nice,hard %O A006967 0,3 %A A006967 _N. J. A. Sloane_ %E A006967 n=2 term corrected June 1996 %E A006967 a(11)-a(20) from Robert Aldred and _Brendan McKay_ %E A006967 More terms from Michal Adamaszek (aszek(AT)mimuw.edu.pl), Aug 22 2006 %E A006967 a(0)=1 prepended by _Alois P. Heinz_, Jan 31 2020 %E A006967 a(41)=1032009647743958000 from _Don Knuth_, Sep 10 2020