cp's OEIS Frontend

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.

A002633 Related to discordant permutations.

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%I A002633 M2384 N0946 #37 Jul 31 2024 09:49:26
%S A002633 1,-3,5,-3,9,-3,-51,-675,-5871,-46467,-331371,-1852227,-920295,
%T A002633 224455293,5571057501,104877816093,1781775072801,28519837563645,
%U A002633 431525731169061,5994769814117757,68879336771960361,346333945918252797,-15047168730918615315,-793523760950138583843
%N A002633 Related to discordant permutations.
%D A002633 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002633 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002633 K. Yamamoto, <a href="https://doi.org/10.2206/kyushumfs.10.1">Structure polynomial of Latin rectangles and its application to a combinatorial problem</a>, Memoirs of the Faculty of Science, Kyusyu University, Series A, 10 (1956), 1-13.
%H A002633 K. Yamamoto, <a href="/A000183/a000183.pdf">Structure polynomial of Latin rectangles and its application to a combinatorial problem</a>, Memoirs of the Faculty of Science, Kyusyu University, Series A, 10 (1956), 1-13. [Annotated scanned copy]
%F A002633 a(n) - (2n-5)*a(n-1) + (n-1)*(n-4)*a(n-2) + (n-1)*(n-2)*a(n-3) = 0.
%F A002633 From _Mélika Tebni_, Mar 02 2022: (Start)
%F A002633 a(n) = Sum_{k=0..n} A213170(k)*A269953(n, k).
%F A002633 E.g.f.: exp(-x*(3 - x) / (1 - x)). (End)
%t A002633 a[ n_ ] := a[ n ]=(2n-5)a[ n-1 ]-(n-1)(n-4)a[ n-2 ]-(n-1)(n-2)a[ n-3 ]; a[ 0 ]=1; a[ 1 ]=-3; a[ 2 ]=5; Table[ a[ n ], {n, 0, 24} ] (* Typo fixed by _Vaclav Kotesovec_, Mar 20 2014 *)
%Y A002633 Cf. A213170, A269953.
%K A002633 sign,easy
%O A002633 0,2
%A A002633 _N. J. A. Sloane_
%E A002633 More terms from _Wouter Meeussen_