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Search: id:A000033
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| A000033 |
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Coefficients of menage hit polynomials.
(Formerly M0602 N0216)
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+0
5
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| 0, 2, 3, 4, 40, 210, 1477, 11672, 104256, 1036050, 11338855, 135494844, 1755206648, 24498813794, 366526605705, 5851140525680, 99271367764480, 1783734385752162, 33837677493828171, 675799125332580020, 14173726082929399560, 311462297063636041906
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 197.
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LINKS
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David W. Wilson, Table of n, a(n) for n = 1..100
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FORMULA
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a(n) = coefficient of t^2 in polynomial p(t) = SUM(k = 0..n, (2n C(2n-k,k) (n-k)! (t-1)^k)/(2n-k))
a(n) = SUM(k = 2..n, ((-1)^k n (2n-k-1)! (n-k)!)/((2n-2k)! (k-2)!)) - David W. Wilson (davidwwilson(AT)comcast.net), Jun 22 2006
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CROSSREFS
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a(n) = n*A000426(n) - Vladeta Jovovic(vladeta(AT)Eunet.yu), Dec 27 2007
A diagonal of A058087. Cf. A000179, A000425.
Adjacent sequences: A000030 A000031 A000032 this_sequence A000034 A000035 A000036
Sequence in context: A037326 A024634 A134305 this_sequence A060411 A037322 A037429
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KEYWORD
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nonn,easy
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AUTHOR
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njas and Simon Plouffe (plouffe(AT)math.uqam.ca)
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EXTENSIONS
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Extended to 34 terms by njas, May 25 2005
Edited and further extended by David W. Wilson, Dec 27 2007
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