%I #9 Jan 30 2024 08:23:48
%S 1,5,35,335,4225,67525,1321075,30751775,832573025,25745985125,
%T 896177819875,34698406783375,1479737530398625,68935386567921125,
%U 3483762766656021875,189846574063623209375,11098195364856546690625,692834276972696475053125
%N Expansion of e.g.f. exp( (5/2) * (1-sqrt(1-4*x)) ).
%F a(0) = 1; a(n) = Sum_{k=0..n-1} 5^(n-k) * (n-1+k)! / (k! * (n-1-k)!).
%F a(n) = 2*(2*n-3)*a(n-1) + 25*a(n-2).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(5/2*(1-sqrt(1-4*x)))))
%Y Cf. A001517, A101682, A243953, A369722, A369723.
%Y Cf. A000108.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jan 30 2024