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A034428
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Coefficients of 1-(1-x)*(tan(x)+sec(x)).
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4
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1, 1, 3, 9, 35, 155, 791, 4529, 28839, 201939, 1542739, 12767689, 113794603, 1086657403, 11068604847, 119790363489, 1372696498127, 16603828720547, 211406514019115, 2826296899863929, 39584082775592211, 579600224535319371
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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COMMENTS
| Also: number of permutations on n elements having the descent pattern: up, up, down, up, down, ...; a(n) = n * E_{n-1} - E_{n} where E_{n} denotes the Euler numbers, see sequence A000111. - Richard Ehrenborg, Feb 12, 2002
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REFERENCES
| R. Ehrenborg and S. Mahajan, Maximizing the descent statistic, Annals Combin., 2 (1998), no. 2, 111-129.
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LINKS
| T. D. Noe, Table of n, a(n) for n = 2..102
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FORMULA
| E.g.f.: 1-(1-x)*(tan(x)+sec(x)).
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MATHEMATICA
| With[{nn=30}, Drop[CoefficientList[Series[1-(1-x)(Tan[x]+Sec[x]), {x, 0, nn}], x]Range[0, nn]!, 2]] (* From Harvey P. Dale, Jan 22 2012 *)
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PROG
| (PARI) a(n)=n!*polcoeff(1-(1-x)*(tan(x+x*O(x^n))+1/cos(x+x*O(x^n))),
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CROSSREFS
| Essentially the same as A131281(n)/2.
Sequence in context: A074507 A030268 A097277 * A101880 A107894 A155858
Adjacent sequences: A034425 A034426 A034427 * A034429 A034430 A034431
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Additional comments from Michael Somos, Dec 03, 2001
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