OFFSET
0,3
COMMENTS
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!}}.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..300
FORMULA
E.g.f.: exp(x/(1-2*x-2*x^2)).
a(n) = n!*sum{i=0..n, sum{j=0..n, 2^j*C(i+j-1,j)*C(j,n-i-j)/i! } }.
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
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
MATHEMATICA
With[{nn=20}, CoefficientList[Series[Exp[x/(1-2x-2x^2)], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 12 2012 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Aug 29 2005
STATUS
approved