Search: id:A028296
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%I A028296
%S A028296 1,1,5,61,1385,50521,2702765,199360981,19391512145,2404879675441,
%T A028296 370371188237525,69348874393137901,15514534163557086905,
%U A028296 4087072509293123892361,1252259641403629865468285
%V A028296 1,-1,5,-61,1385,-50521,2702765,-199360981,19391512145,-2404879675441,
%W A028296 370371188237525,-69348874393137901,15514534163557086905,
%X A028296 -4087072509293123892361,1252259641403629865468285
%N A028296 Expansion of Gudermannian(x) = 2*arctan(exp(x))-Pi/2.
%C A028296 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
%C A028296 This sequence is also EulerE[2 n]. - Paul Abbott (paul(AT)physics.uwa.edu.au), 
               Apr 14 2006
%D A028296 Gradshteyn and Ryzhik, Tables, 5th ed., Section 1.490, pp. 51-52.
%H A028296 N. E. Noerlund, <a href="http://www-gdz.sub.uni-goettingen.de/cgi-bin/
               digbib.cgi?PPN373206070">Vorlesungen ueber Differenzenrechnung</a> 
               Springer 1924, p. 25.
%F A028296 E.g.f.: sech x or gd x.
%F A028296 Recurrence: a(n) = -Sum[i=0..n-1, a(i)*C(2n, 2i) ]. - Ralf Stephan, Feb 
               24 2005
%e A028296 gd x = x - 1/6*x^3 + 1/24*x^5 - 61/5040*x^7 + 277/72576*x^9 + ....
%t A028296 Table[EulerE[2 n], {n, 0, 30}] - Paul Abbott (paul(AT)physics.uwa.edu.au), 
               Apr 14 2006
%Y A028296 Essentially same as A000364.
%Y A028296 Cf. A000364.
%Y A028296 Sequence in context: A065919 A096537 A115047 this_sequence A000364 A159316 
               A116163
%Y A028296 Adjacent sequences: A028293 A028294 A028295 this_sequence A028297 A028298 
               A028299
%K A028296 sign,easy,nice
%O A028296 0,3
%A A028296 N. J. A. Sloane (njas(AT)research.att.com).

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