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A002633
Related to discordant permutations.
(Formerly M2384 N0946)
0
1, -3, 5, -3, 9, -3, -51, -675, -5871, -46467, -331371, -1852227, -920295, 224455293, 5571057501, 104877816093, 1781775072801, 28519837563645, 431525731169061, 5994769814117757, 68879336771960361, 346333945918252797, -15047168730918615315, -793523760950138583843
OFFSET
0,2
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
K. Yamamoto, Structure polynomial of Latin rectangles and its application to a combinatorial problem, Memoirs of the Faculty of Science, Kyusyu University, Series A, 10 (1956), 1-13.
K. Yamamoto, Structure polynomial of Latin rectangles and its application to a combinatorial problem, Memoirs of the Faculty of Science, Kyusyu University, Series A, 10 (1956), 1-13. [Annotated scanned copy]
FORMULA
a(n) - (2n-5)*a(n-1) + (n-1)*(n-4)*a(n-2) + (n-1)*(n-2)*a(n-3) = 0.
From Mélika Tebni, Mar 02 2022: (Start)
a(n) = Sum_{k=0..n} A213170(k)*A269953(n, k).
E.g.f.: exp(-x*(3 - x) / (1 - x)). (End)
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A199668 A318377 A186203 * A070554 A076842 A077862
KEYWORD
sign,easy
EXTENSIONS
More terms from Wouter Meeussen
STATUS
approved