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A112241 Expansion of exp(x/(1-2x-2x^2)). 1

%I

%S 1,1,5,49,601,9281,170941,3662065,89368049,2446433281,74212220341,

%T 2470200090161,89490288001225,3504680581915969,147513939627740141,

%U 6639918363792119281,318237954786998696161,16178761263710217424385

%N Expansion of exp(x/(1-2x-2x^2)).

%C In general, e.g.f. exp(x/(1-ax-bx^2)) has general term n!*sum{i=0..n, sum{j=0..n, a^j*(b/a)^(n-i-j)*C(i+j-1,j)C(j,n-i-j)/i!}}.

%H Harvey P. Dale, <a href="/A112241/b112241.txt">Table of n, a(n) for n = 0..300</a>

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

%F a(n) = n!*sum{i=0..n, sum{j=0..n, 2^j*C(i+j-1,j)*C(j,n-i-j)/i! } }.

%F Recurrence: a(n) = (4*n-3)*a(n-1) - 2*(n-2)*(n-1)*(4*n-13)*a(n-3) - 4*(n-4)*(n-3)*(n-2)*(n-1)*a(n-4). - _Vaclav Kotesovec_, Aug 15 2013

%F a(n) ~ 2^(-3/4)*3^(-1/8) * (1+sqrt(3))^n * exp(3^(-1/4)*sqrt(2*n)-n-1/12) * n^(n-1/4) * (1-7/(6*3^(3/4)*sqrt(2*n))). - _Vaclav Kotesovec_, Aug 15 2013

%t With[{nn=20},CoefficientList[Series[Exp[x/(1-2x-2x^2)],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, May 12 2012 *)

%K easy,nonn

%O 0,3

%A _Paul Barry_, Aug 29 2005

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Last modified January 27 05:35 EST 2021. Contains 340455 sequences. (Running on oeis4.)