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Expansion of the exponential series exp( x * T(x) ) = exp( x / sqrt(1 - 2*x - 3*x^2) ), where T(x) is the ordinary generating series of the central trinomial coefficients (A002426).
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%I #14 Feb 28 2017 22:33:59

%S 1,1,3,25,265,3741,64051,1298053,30295665,800411545,23601417571,

%T 768200763441,27352316065273,1057402991121205,44102326806885075,

%U 1973793512480683741,94345589402816289121,4796647490592139950513

%N Expansion of the exponential series exp( x * T(x) ) = exp( x / sqrt(1 - 2*x - 3*x^2) ), where T(x) is the ordinary generating series of the central trinomial coefficients (A002426).

%H G. C. Greubel, <a href="/A080896/b080896.txt">Table of n, a(n) for n = 0..379</a> (terms 0..100 from T. D. Noe)

%F E.g.f.: exp(x/sqrt(1 - 2*x - 3*x^2)).

%t With[{nn=20},CoefficientList[Series[Exp[x/Sqrt[1-2 x-3x^2]],{x,0,nn}], x]Range[0,nn]!] (* _Harvey P. Dale_, Sep 08 2011 *)

%o (PARI) x='x + O('x^50); Vec(serlaplace(exp(x/sqrt(1 - 2*x - 3*x^2)))) \\ _G. C. Greubel_, Feb 27 2017

%Y Cf. A002426.

%K easy,nice,nonn

%O 0,3

%A _Emanuele Munarini_, Mar 31 2003