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A112240 Expansion of exp(x/(1-x-2x^2)). 0

%I

%S 1,1,3,25,217,2541,34531,550453,9957585,202137337,4543312771,

%T 112004037201,3003936136873,87057179039845,2710682505789987,

%U 90230919126896941,3197152300287286561,120131212083966304113

%N Expansion of exp(x/(1-x-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!}}.

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

%F a(n) = (2*n-1)*a(n-1) + 3*(n-2)*(n-1)*a(n-2) - 2*(n-2)*(n-1)*(2*n-7)*a(n-3) - 4*(n-4)*(n-3)*(n-2)*(n-1)*a(n-4). - _Vaclav Kotesovec_, Sep 25 2013

%F a(n) ~ 3^(-1/4) * n^(n-1/4) * 2^(n-1/2) * exp(2*sqrt(n/3)-n-1/18) * (1 - 263/(432*sqrt(3*n))). - _Vaclav Kotesovec_, Sep 25 2013

%t CoefficientList[Series[E^(x/(1-x-2*x^2)), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Sep 25 2013 *)

%K easy,nonn

%O 0,3

%A _Paul Barry_, Aug 29 2005

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Last modified February 25 22:37 EST 2021. Contains 341618 sequences. (Running on oeis4.)