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A112240
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Expansion of exp(x/(1-x-2x^2)).
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0
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1, 1, 3, 25, 217, 2541, 34531, 550453, 9957585, 202137337, 4543312771, 112004037201, 3003936136873, 87057179039845, 2710682505789987, 90230919126896941, 3197152300287286561, 120131212083966304113
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OFFSET
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0,3
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COMMENTS
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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!}}.
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LINKS
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FORMULA
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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!}};
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
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
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MATHEMATICA
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CoefficientList[Series[E^(x/(1-x-2*x^2)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 25 2013 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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