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%I #14 Jul 12 2023 11:23:58
%S 1,2,4,48,384,1920,46080,129024,1032192,185794560,3715891200,
%T 40874803200,78479622144,10202350878720,64924051046400,
%U 42849873690624000,1371195958099968000,4662066257539891200,335668770542872166400,5797915127558701056000
%N Denominators of expansion of exp(1-sqrt(1-x-2*x^2)).
%H Robert Israel, <a href="/A144578/b144578.txt">Table of n, a(n) for n = 0..404</a>
%F A144577/A144578 is D-finite with recurrence 64*b(n) + 48*b(n+1) + (32*n^2 + 96*n + 76)*b(n+2) + (24*n^2 + 120*n + 145)*b(n+3) + (-12*n^2 - 66*n - 72)*b(n+4) + (-4*n^2 - 36*n - 80)*b(n+5)=0. - _Robert Israel_, Dec 17 2020
%e 1 + (1/2)*x + (5/4)*x^2 + (55/48)*x^3 + (757/384)*x^4 + (4973/1920)*x^5 + (...
%p f:= gfun:-rectoproc({64*a(n) + 48*a(n + 1) + (32*n^2 + 96*n + 76)*a(n + 2) + (24*n^2 + 120*n + 145)*a(n + 3) + (-12*n^2 - 66*n - 72)*a(n + 4) + (-4*n^2 - 36*n - 80)*a(n + 5), a(0) = 1, a(1) = 1/2, a(2) = 5/4, a(3) = 55/48, a(4) = 757/384},a(n),remember):
%p map(denom@f, [$0..30]); # _Robert Israel_, Dec 17 2020
%t CoefficientList[Series[Exp[1-Sqrt[1-x-2x^2]],{x,0,20}],x]//Denominator (* _Harvey P. Dale_, Jul 12 2023 *)
%Y Cf. A144577.
%K nonn,frac
%O 0,2
%A _N. J. A. Sloane_, Jan 07 2009
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