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%I #23 Nov 14 2013 18:03:31
%S 1,1,2,4,11,31,110,400,1757,7861,41402,220540,1358183,8405203,
%T 59340710,418689544,3335855897,26440317193,234747589106,2065458479476,
%U 20224631361251,195625329965671,2094552876276830,22092621409440256
%N Binomial transform of reduced tangent numbers (A002105).
%C Hankel transform is A154604.
%H Vincenzo Librandi, <a href="/A154603/b154603.txt">Table of n, a(n) for n = 0..300</a>
%F G.f: 1/(1-x-x^2/(1-x-3x^2/(1-x-6x^2/(1-x-10x^2/(1-x-15x^2..... (continued fraction);
%F E.g.f.: exp(x)*(sec(x/sqrt(2))^2);
%F G.f.: 1/(x*Q(0)), where Q(k)= 1/x - 1 - (k+1)*(k+2)/2/Q(k+1); (continued fraction). - _Sergei N. Gladkovskii_, Apr 26 2013
%F G.f.: 1/Q(0), where Q(k)= 1 - x - 1/2*x^2*(k+1)*(k+2)/Q(k+1); (continued fraction). - _Sergei N. Gladkovskii_, May 04 2013
%F a(n) ~ n! * 2^(2+n/2)*n*(exp(sqrt(2)*Pi)+(-1)^n) / (Pi^(n+2)*exp(Pi/sqrt(2))). - _Vaclav Kotesovec_, Oct 02 2013
%F G.f.: T(0)/(1-x), where T(k) = 1 - x^2*(k+1)*(k+2)/(x^2*(k+1)*(k+2) - 2*(1-x)^2/T(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Nov 14 2013
%t With[{nn=30},CoefficientList[Series[Exp[x]Sec[x/Sqrt[2]]^2,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, May 30 2013 *)
%K easy,nonn
%O 0,3
%A _Paul Barry_, Jan 12 2009
%E Typo in e.g.f. fixed by _Vaclav Kotesovec_, Oct 02 2013
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