This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A369724 #9 Jan 30 2024 08:23:48
%S A369724 1,5,35,335,4225,67525,1321075,30751775,832573025,25745985125,
%T A369724 896177819875,34698406783375,1479737530398625,68935386567921125,
%U A369724 3483762766656021875,189846574063623209375,11098195364856546690625,692834276972696475053125
%N A369724 Expansion of e.g.f. exp( (5/2) * (1-sqrt(1-4*x)) ).
%F A369724 a(0) = 1; a(n) = Sum_{k=0..n-1} 5^(n-k) * (n-1+k)! / (k! * (n-1-k)!).
%F A369724 a(n) = 2*(2*n-3)*a(n-1) + 25*a(n-2).
%o A369724 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(5/2*(1-sqrt(1-4*x)))))
%Y A369724 Cf. A001517, A101682, A243953, A369722, A369723.
%Y A369724 Cf. A000108.
%K A369724 nonn
%O A369724 0,2
%A A369724 _Seiichi Manyama_, Jan 30 2024