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Search: id:A028296
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| A028296 |
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Expansion of Gudermannian(x) = 2*arctan(exp(x))-Pi/2. |
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+0
6
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| 1, -1, 5, -61, 1385, -50521, 2702765, -199360981, 19391512145, -2404879675441, 370371188237525, -69348874393137901, 15514534163557086905, -4087072509293123892361, 1252259641403629865468285
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The first column of the inverse to the matrix with entries C[2 i,2 j], i,j >=0. The full matrix is lower triangular with the i-th sundiagonal having entries a[i]C[2j,2i] j=i,i+1,... - Nolan Wallach (nwallach(AT)ucsd.edu), Dec 26 2005
This sequence is also EulerE[2 n]. - Paul Abbott (paul(AT)physics.uwa.edu.au), Apr 14 2006
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REFERENCES
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Gradshteyn and Ryzhik, Tables, 5th ed., Section 1.490, pp. 51-52.
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LINKS
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N. E. Noerlund, Vorlesungen ueber Differenzenrechnung Springer 1924, p. 25.
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FORMULA
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E.g.f.: sech x or gd x.
Recurrence: a(n) = -Sum[i=0..n-1, a(i)*C(2n, 2i) ]. - Ralf Stephan, Feb 24 2005
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EXAMPLE
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gd x = x - 1/6*x^3 + 1/24*x^5 - 61/5040*x^7 + 277/72576*x^9 + ....
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MATHEMATICA
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Table[EulerE[2 n], {n, 0, 30}] - Paul Abbott (paul(AT)physics.uwa.edu.au), Apr 14 2006
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CROSSREFS
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Essentially same as A000364.
Cf. A000364.
Sequence in context: A065919 A096537 A115047 this_sequence A000364 A159316 A116163
Adjacent sequences: A028293 A028294 A028295 this_sequence A028297 A028298 A028299
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KEYWORD
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sign,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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